Quality of life in French cities

Measuring the je ne sais quoi

Mylène Feuillade∗ Under the supervision of Pierre-Philippe Combes

A thesis presented for the degree of Master in Economics

Department of Economics QEM, Erasmus Mundus Sciences Po Paris Université Paris I

22 May, 2018

∗I would like to sincerely thank Pierre-Philippe Combes for agreeing to supervise me, and for his time, comments and invaluable advices during the project. I am also extremely grateful to Paul Bouche, Sophie Nottmeyer, Manola Zabalza, Marie Cases and Zydney Wong for their help and support.

Abstract

This paper aims at estimating the quality of life in French cities from a revealed- preference approach. Using official city-level data on wages and amenities, as well as web-scrapped information on housing prices, we perform a two-step analysis. First, we study how rents and wages co-vary to estimate quality of life. We then use those results to find out how households value amenities. We prove that using a direct measure of available income to model households’ location choices or trying to replicate expected wage produces very similar results in terms of quality of life estimation. Overall we find that cities in Southern France and in the Alps offer the highest quality of life, while areas in rural regions of central France fare worst. Households appear to highly value proximity to the shore and mild-winters. Easy access to cultural amenities and health services is also found to significantly impact quality of life.

2 Contents

Introduction 5

1 A model of households residential choice6 1.1 Using available income...... 6 1.2 Expected Wages...... 8 1.3 Empirical strategy...... 9

2 Data 10 2.1 Sampling...... 10 2.2 Income and wages...... 10 2.3 Housing prices...... 11 2.4 Amenities...... 12 2.5 Other data...... 12

3 Limitations 12 3.1 Limitations of the model...... 12 3.2 Limitations of the empirical strategy: identification problems...... 13

4 First-step regressions: Wages and rent gradients 14 4.1 Rent estimates...... 14 4.2 Wages and income...... 16 4.3 On the way to expected wages: unemployment and tax rate...... 19 4.4 Is there a bell curve?...... 21

5 Indexes of Quality of Life 23 5.1 Testing the parameters in the quality of life equation...... 23 5.2 Quality of Life indexes...... 25

6 The determinants of Quality of Life 31

Conclusion 38

Bibliography 39

Appendixes 41

A Visualisation of the wage and rent gradients 41

B Further insights into the bell curve 43

C Quality of life: difference between rankings 46

D Quality of life: full rankings across Urban Areas 47

E Results at the Urban Unit level 55

3 List of Tables

1 Housing price and city size, across Urban Area...... 15 2 Wage and density across Urban Areas...... 17 3 Wage and city size (across Urban Area)...... 17 4 Available income and city size (across Urban Area)...... 18 5 Unemployment and city size across Urban Areas...... 20 6 Tax rate and city size across urban areas...... 21 7 Bell curve: net wage and city size (Urban Areas)...... 22 8 Housing price and available income by Urban Areas...... 23 9 Housing price and expected wage by Urban Areas...... 25 10 Quality of Life in Urban Areas, computed with income and constant share of housing 26 11 Quality of Life in Urban Areas, computed with income and variable share of housing 27 12 Quality of Life in Urban Areas, computed with wage and constant share of housing 29 13 Quality of Life in Urban Areas, computed with wage and variable share of housing 31 14 Correlation matrix between QoL rankings (Urban Areas)...... 32 15 Predictive power of amenities on Quality of Life (computed from income)..... 36 16 Predictive power of amenities on Quality of Life (computed from expected wage). 37

List of Figures

1 Quality of life: housing costs versus available income...... 28 2 Quality of life: housing costs versus expected wage...... 30

4 Introduction

Households deciding on their city of residence need to strike a balance between highly-paid jobs, good quality of life and low housing costs. Those three elements are often difficult to obtain together, since desirable areas in terms of amenities are generally expensive. This paper seeks to exploit this threefold relationship, and uses information on rents and revenues to develop a quality of life index of French cities, based on households’ willingness to pay to live in a city. Because households are heterogeneous and imperfectly mobile, and because quality of life is a complex concept containing many subjective components, this index can only provide a limited perspective on an intricate question. Nevertheless, it provides an economic intuition and results that are in line with popular expectations on quality of life, with urban areas in Southern France or in the Alps being ranked highest, and cities located in decaying regions of central France being ranked lowest. The literature on quality of life is large, and generally relies on the assumption that quality of life can be measured as a weighted average of amenities. The obvious question is then how to determine the weights of each amenities. An empirical answer to that question builds on the theory by Tiebout (1956) that households "vote by their feet" and will move to the area that fits best their preferences for publicly-provided goods. By assuming that households are fully mobile and perfectly informed, it then becomes possible to evaluate the valuation of such publicly provided goods, or amenities, from the workers’ location choice. If people can vote with their feet and move freely to the place that maximises their utility, it follows that in equilibrium, no one could be made better-off by moving to a new city. Rosen (1979) was the first to use this type of model to implicitly estimate the valuation of amenities through the analysis of wage variation across areas. The intuition behind his method is that in spatial equilibrium households are only willing to accept lower wages in exchange for better amenities. Studying how wages co-vary with amenities hence allows to estimate how much households are willing to pay to access an amenity. Rosen then used the computed valuation to weight amenities and construct a quality of life index that was directly determined from the workers’ observed behaviour. Roback (1982) later extended this model to include variation in rents, arguing that the worker could pay for access to amenities both through lower wages and through higher rents. She hence used co-variance in wages, rents and amenities to directly estimate household’s valuation of amenities, and then compute a quality of life index. Since then a large number of quality of life indexes have been developed based on the co- variation of wages, rents and amenities, mainly on US data (Berger, Blomquist, and Waldner, 1987, Blomquist et al., 1988, Chen et al., 2008...). Albouy (2008) builds on the Rosen-Roback model of compensating differentials, and improves it with three adjustments. First, he tries to account for differences in cost of living that do not stem from rents. Second, he incorporates into the model sources of income other than wages, that do not depend on location. Finally, he introduces taxes into his quality of life equation. With those three amendments, he obtains a quality of life ranking that is more believable and more in line with the non-academic literature on areas’ livability than the previous estimates. He then regresses quality of life on some amenities, to deduce their valuation by households. This two-steps estimation

5 is the reverse of the approach by Roback (1982) who estimated valuation of amenities and used those results to estimate quality of life. The method we use in this paper, following Albouy, has the advantage that it does not require any assumptions on which amenities are most valued by households and should be included in the computation of a quality of life index. Therefore, it does not rely either on the availability of data on a large range of amenities. Most of the literature on quality of life focuses on US data. Some studies have previously been done in Russia (Berger, Blomquist, and Peter, 2008), Germany (Buettner et al., 2009), or Italy (Colombo et al., 2014), but to the best of our knowledge no hedonic quality of life rankings has ever been computed on French data. This might be simply be due to a lack of availabe data on housing prices, a core element of the revealed-preferences approach. Another specificity of the European case, is the relative immobility of European workers. Cheshire et al. (2006) argue that European households are less mobile than their American counterparts, which would weaken the theoretical foundation of the revealed-preference. However, the authors also find that population movement within European countries does respond to quality of life differences, and in particular to climate. There is hence some space to try and estimate a compensating differentials model within countries. In this paper, we will try to use Albouy’s (2008) model on French data, with a few amendments to the model. First, differences in wages are replaced by difference in available income, which is what Albouy tries to recreate when he incorporates taxes and non-wage revenues. We will also compute differences in expected wages, which include city-dependent taxes and unemployment rate, to obtain an alternative quality of life measure. Those amendments are presented in the first section of this paper. Section2 presents the data we used. Section3 explains the limitations of our analysis, and details the endogeneity issues we face in our estimations. Section4 is used to compute comparable housing prices and incomes, which are net of education effects. We also test in this section whether net wages in French cities exhibit the bell shaped curve predicted by theory. Section5 presents our quality of life indexes, while section6 regress those estimates on various amenities to try to determine their valuation by households.

1 A model of households residential choice

We use the model developed by Albouy (2008) and slightly adapt it, to replace wages first with available income and then with expected wages.

1.1 Using available income

Households characteristics and preferences

Households are homogeneous, fully mobile, and have full information about the conditions of life H in different cities, indexed c. For each city they observe: the price of housing pc ; the price of x k other consumption goods p , assumed to be a numeraire; k amenities Ac , regrouped into an index ˜ k Qc = Q(Ac ), referred to as "quality of life"; and the final income they would earn in that city, yc. Households supply one unit of labour in their city of residence, in exchange for this final income which includes wages wc, taxes τc, and the external income that does not come from wages I. External income is assumed to be independent of the household’s place of residence.

6 From those observations, the households choose their city of residence c and their consumption of housing H and other consumption goods x. Households have utility U(x, H; Qc) which is increasing and quasi concave in x, H, and Q. Hence the budget constraint of a household is

H x pc H + p x ≤ yc

with yc = (1 − τc)(wc + I)

The expenditure function can be defined as:

H x H x E(pc , p , yc, u; Qc) = min{pc H + p x − yc | U(x, H; Qc) ≥ u} H,x

It represents the minimum net expenditure that a household needs to make in order to reach utility level u in city c.

Equilibrium

Households are homogeneous and fully mobile by assumption, so in equilibrium the utility must be equalised in all cities at level u¯. This means that no household needs to make extra expenditure in order to reach utility u¯. This equilibrium condition can be characterised using the expenditure function:

H x ∀c E(pc , p , yc, u¯; Qc) = 0 (1)

¯H ¯ Differentiating equation (1) around national averages pc y¯c and Qc yields the following condi- tion.

∂E H x H ∂E H x ∂E H x ∀c H (pc , p , yc, u¯; Qc).dpc + (pc , p , yc, u¯; Qc).dyc + (pc , p , yc, u¯; Qc).dQc = 0 (2) ∂pc ∂yc ∂Qc

H with dpc , dyc, and dQc representing deviation from the national average in city c. Applying Shephard’s lemma we obtain :

Q ∗ H x H ∀c pc dQc = H (pc , p , u¯).dpc − dyc (3)

Q ∂E H x where p = − (p , p , yc, u¯; Qc) represents the marginal valuation of amenities by households ; c ∂Qc c ∗ H x and H (pc , p , u¯) is the Hicksian demand for housing. Evaluating this at the national average we get:

Q ¯ H pc dQc = H.dpc − dyc (4) where H¯ is the national average of housing expenditures. This equation illustrates how a higher available income compensates workers for higher living costs or lower amenities. Conversely, higher living costs are paid by households in order to access better amenities, or a higher income.

7 Operationalisation

We can use equation (4) as a basic index of quality of life. In order to render it operational, we dpH H c divide the equation by y¯ the average available income, and we define the log-differentials pcc = H p¯c Q dyc pc ; yc = . We also define Qcc = dQc, the fraction of average income that households are willing b y¯ y¯ to pay for a marginal increase in their quality of life. Evaluating this at the national average allows us to create a unified index Inserting this into equation (4) yields the final equation

¯ ¯H Hpc H Qcc = .pc − yc y¯ c b H =s ¯H pcc − ybc (5) where s¯H is the average share of income that is spent on housing goods. In his article, Albouy (2008) uses variation in wage instead of available income, that he then weights down to account for taxation and the relative importance of other sources of income. The advantage of the model above is that it considers variation in available income, which already includes all those elements and does not require any assumptions on average tax rate or on the share of income that stems from labour. Nevertheless, in a later part of the analysis we also compute a wage-based quality of life index founded on the following model.

1.2 Expected Wages

The model using wage is very similar to the one introduced above. Households are again homoge- neous, fully mobile and fully informed. Following the intuition of Harris et al. (1970), we further assume that households make their location choice based on expected income, taking into account unemployment levels. Albouy chose to ignore the city employment rate in his model, but we sus- pect that it might be a relevant factor in households migration in France, where unemployment is higher than in the United States. Households provide one unit of labour in their city of residence, in exchange of which they receive a wage wc. In addition, they observe the unemployment rate uc and tax rate τc in all cities, and deduce from this their expected wage w˜c = (1 − τc)(1 − uc)wc. We assume now that tax only applies to labour income. The households’ total income in city c is then w˜c + I. The assumptions on prices and the shape of the utility functions are the same as before. With those amendments, the expenditure function becomes:

H x H x E(pc , p , w˜c, u; Qc) = min{ pc H + p x − (w ˜c + I) | U(x, H; Qc) ≥ u } H,x

From the assumption that households are fully mobile, we know that the utility must be H x equalised at level u¯, and E(pc , p , w˜c, u¯; Qc) = 0. Differentiating this condition around the national ¯H ¯ ¯ averages pc , w˜c and Qc, and applying Shephard’s Lemma, we obtain the following condition:

Q ¯ H pc dQc = H.dpc − dw˜c (6)

8 H Q dp dw˜c p H c c Defining as previously pc = ; w˜c = and Qc = dQc, and dividing the equation by c ¯H c ¯ c pc w˜c y¯ average income y¯ we reach our quality of life equation:

¯ ¯H ¯ Hpc H w˜c Qcc = .pc − .wc˜c y¯ c y¯ H =s ¯H pcc − s¯wwc˜c (7) where sH is the housing expenditure share out of total income, and sw is the share of income that comes from labour.

1.3 Empirical strategy

To estimate equations (5) and (7), we need to select the correct parameters s¯H and s¯w, and to compute the log differentials for housing prices, available income, and expected wages.

For the share of housing in expenditure s¯H we use the result of Combes, Duranton, et al. (2012) who find a share of 32.5% for a city of average size in France. Their results are also used to compute in parallel another index in which the share of housing in expenditure varies with cities’ population. We use their preferred coefficient of 0.048 on city population to compute the share of Nc ¯ a city as sH = 0.325 + 0.048ln( N¯ ), with Nc the population in city c and N the average of city size in the subsample. This is only done on the 200 largest cities in our sample cities because it broadly corresponds to the sample used by the authors in their regressions. Using the smallest cities in our sample leads to a logarithm too negative, and a negative share of housing in expenditure in those cities. While we did not find a satisfying way to incorporate a share of housing that varies with city into the theoretical model, the intuition behind this empirical specification is that if households spend a larger share of their income on housing in larger cities it will increase the urban costs for those cities. Fully informed households should know that they will spend relatively more on housing in some cities, and should take that into account when making a residence choice. We find however that the results on quality of life are not significantly changed when including a variable share of housing in expenditure. To estimate equation (7), we use an average share of wages in available income of 0.53 in 2014, computed from national level data provided by the French Statistical Institute∗. In order to partially control for the sorting of people into different cities according to skills, which Combes, Duranton, et al. (2008) have demonstrated to be a strong determinant of spatial wage disparities in France, we compute the differentials of income and expected wage net of the effect of education. To do this, we first regress income, wage and unemployment in an urban area on characteristics of the area: population, education and land area. The results of those first-step regressions are reported in section4. The obtained coefficients are used to render the variables net of education. We then compute the log differentials as the deviation from the national average. The same strategy is used to compute housing prices net of education effect.

∗Tableaux de l’économie française, revenus des ménages, found at this address: https://www.insee.fr/fr/statistiques/3303428?sommaire=3353488

9 2 Data

2.1 Sampling

The main geographical level of the analysis is urban areas in mainland France. In its 2010 version, the definition of French geographical units provided by the National Institute of Statistics and Economic Studies (INSEE) defines 760 urban areas. Out of those, only 609 have available housing costs data. The urban areas we lose all have less than 50,000 inhabitants. Because the data on housing prices is only available at the urban unit level we also perform all our analysis for urban units, to check that this geographical discrepancy does not affect the results. All the graphs and tables at the Urban Unit level can be found in AppendixE. According to the 2010 definition by the National Institute of Statistics there are 2217 urban units in mainland France. We only have housing cost data for 1397 of those. All the urban units we leave out due to this lack of data have population below 27,000. Urban units are defined as a set of municipalities which contains a built area of at least 2,000 inhabitants, with no housing being more than 200 meters away from its closest neighbour. Urban areas are defined around a central urban unit of at least 1500 jobs, and include all the surrounding municipalities of which at least 40% of the population works in the urban unit or associated municipalities. We use these definitions to find the set of urban units that are at the centre of an Urban Area on which we later perform the urban unit analysis.

2.2 Income and wages

We use two different specification of income in our analysis: available income, and average net hourly wage. Both are available from the French National Institute of Statistics and Economic Studies. The data on average net hourly wage in 2014 is obtained from the Annual Declaration of Social Data (Déclaration annuelle de données sociale, DADS). This is an administrative database that is collected from a yearly declaration compulsory for all French employers, containing information on their employees and their establishment. The hourly wage data is available directly at both the urban unit and urban area levels. Hourhly wage is calculated as the quotient of the yearly wage on the total of hours paid including overtime, as well as paid holidays, sick days... The net hourly wage is attached to the worker’s place of residence. For available income, we use data from the Localised Social and Fiscal File (Fichier localisé social et fiscal, FiLoSoFi). This data set is managed by the National Institute of Statistics and Economic Studies. It gathers administrative data on fiscal matters from the French General Di- rectorate of Public Finances (Direction Générale des Finances Publiques), as well as information on social allowance from several benefit funds (National Family Allowance Fund (Cnaf), National Old-age Insurance Fund (Cnav), and Central Agricultural Social Mutual Fund (CCMSA)). For each urban unit and for each urban area, the FiLoSoFi data set provides characteristics of the distribution of available income per consumption unit in 2014 (in particular the median). A household’s available income includes all of its revenues (work-related or not), net of social contributions on wages and of taxes. This available income is divided by the number of consumption units in the household, in order to be able to compare households that are composed differently.

10 Both available income and mean wage are available for all urban units and all urban areas save one. Information from the FiLoSoFi data set was also used to compute a tax rate per urban area and urban unit.

2.3 Housing prices

There is no official publicly available data on housing prices at the municipality, urban unit or urban area level in France. Notaries record information on housing price and characteristics for all transactions they make, but this data is not easily accessible. However the High Council of French Notaries (Conseil Supérieur du Notariat), the official organisation representing all notaries, allows users of their website† to explore the map of France and get information on housing prices in different areas and for different types of goods. The different categories available are type of building (house, apartment, apartment block, bare land...), age (new or already existing building), number of rooms, surface, and availability of a parking slot. We took advantage of this opportunity and performed web scrapping operations on their website. The notary website provides access to this data at different geographical levels: neighbourhood, municipality, urban unit, department... but not at the urban area level. It is important to note that the notaries only publish data for a type of good in an area if more than 20 such transactions occurred in the area during the time period. For this reason, the more we narrowed the criteria, the less observations we could collect. As a result, we decided to only focus on the broadest geographical scale that is still relevant to the study of cities: urban units. We also decided to only exploit the possibility of filtering goods by their age. All other criteria were too narrow and would have allowed us to collect data on very few urban units. We built an algorithm using R that allowed us to retrieve all the html code of a web page, as well as all the information processed by javascript but hidden in the html code. We then extracted from the obtained code the median price per square meter in the area. When an area for which no data is available is selected, the website automatically enlarges the criteria, both for the geography (going from municipality to department for instance) and for the housing characteristics (going to 5-rooms houses to all houses). We had to ensure that such results were not recorded in the data set created. We applied this algorithm to all French urban units, for five different type of transactions: new houses, new apartments, existing houses, existing apartments, and existing houses and apartments together. After the data collection we observed that only this last group (old houses and apartments grouped together) yielded data for more than half of the urban units. It might have been better to supplement this variable with one on the price of new housing, but only 6% of urban units had data on new apartments, and for new houses this proportion fel to less than 2%. The data obtained from the website concerns the last trimester of 2017 (from the 1st of October, to the 31st of December). It is corrected for seasonal variations by the notaries before they publish it. It is also cleaned to exclude unusual goods such as castles or extremely small attic rooms. To obtain a measure of price in an urban area, we averaged prices in all urban units comprised

†https://www.immobilier.notaires.fr/

11 in the urban area, weighted by population.

2.4 Amenities

Artifical amenities: For artificial amenities, we use data on the year 2016 from the French Perma- nent Census of Equipements (Banque Permanente des Equipements, BPE). The data is available at the municipality scale, and we aggregate it at the urban area and urban unit levels. The data is maintained by the National Institute of Statistics and Economic Studies. The primary data sources are the National Registry of Establishments (siren) for retail establishments such as restaurants and cinemas; the French Ministry for Education for primary, middle, high schools, and universities; the French Ministry of Culture for museums; and the Ministry of health for doctors, hospitals and medical services. Climate: Climate data originally comes from the ATEAM European project. We only obtained it aggregated at the département level. The value of climate variables for an urban area (resp urban unit) is computed by associating each municipality to the value of its département, and calculating the average of municipalities within the urban area (resp urban unit) weighted by land area.

2.5 Other data

Unemployment: The unemployment rate per city was computed using information from the 2014 census on the number of unemployed persons per municipalities, and the size of the labour force. Land Area: In order to compute the land area of cities, we use the the GEOFLA data set provided by the French National Geographical Institute. It contains land area information for all French municipalities, and we aggregated this data to obtain the land area of urban area and urban units.

3 Limitations

We acknowledge a number of limitation to our analysis, both in the theoretical model and in the emprical approach we adopt.

3.1 Limitations of the model

The standard concept of equilibrium we use in which utility is equalised across geographical units and among homogeneous households has strong weaknesses. First, it requires the assumption that households are perfectly mobile, which is not verified in real life: moving to a new city incurs a various costs, in terms of money, time and even social networks. Consequently, households will only take advantage of a difference in utility between two cities if their expected utility gain is greater than the cost of moving. This is confirmed empirically in the US by Berger and Blomquist (1992) who find that moving costs matter in households’ decision to move or not. Furthermore, the assumption that households have full information about their location options is also unlikely to be true, furthering the chance that some potential utility discrepancy between cities could remain even in equilibrium.

12 The imperfect mobility of households is also reinforced by idiosyncratic preferences. While we assumed that households were homogeneous, individuals might actually have a special link to their city of birth, or a preference for a certain local culture or a type of climate, which means that they would differ in their valuation of certain amenities. This weakens the analysis performed in section 6, in which the valuation of some amenities is estimated for typical households. Life cycle effects could also be a source of heterogeneity among households.As exemplified by Chen et al. (2008), households at different point in their life cycle do not choose their location residence based on the same criteria. A family with young children would probably put more weight on wages in their decision, while retired people should be concerned solely with housing costs and amenities. We do not control for this life cycle effect in our analysis. Our model also relies on the assumption that consumption goods other than housing have constant prices across cities. This simplification can be defended using empirical work by Handbury et al. (2014) who demonstrated that once variety is taken into account the price of groceries in the US does not vary significantly with city size.

3.2 Limitations of the empirical strategy: identification problems

A major issue faced in the analysis is that of endogeneity, which arises at several levels. A first concern in our wages and rents regression is the possibility that some variables which are correlated with both wages (or rents) and city size are not included in the equation. While we do control for the sorting of households according to education, our variable for education consists in the share of the population with a higher education degree, which is quite imprecise and does not capture very precisely the skills of workers in a city. It is hence very likely that there is some sorting due to unobserved skills that we do not control for. Furthermore, households might sort into cities according to other variables than education, such as the industry they work in. A large city such as Paris concentrates more highly paid industries like finance. One could consider this to be a direct effect of agglomeration, with larger cities offering some advantages that make them more attractive to highly-rewarding industries, in which case industry composition should not be controlled for in our regressions. Yet, if we consider that this concentration is due to historical or political reasons, then it means that the higher wages we observe in larger cities are not due to agglomeration economies. In that case, it would be better to control for the industrial composition of the city, to compare identical workers in identical industries. We chose not to control for industry composition due to the lack of appropriate data, but fully recognise that this might not necessarily be the "correct" way estimate the elasticity of wages with respect to city size. Another concern in our analysis is the question of reverse causality. The implicit assumption in our wage regressions is that the higher level of wages empirically observed in larger city is due to agglomeration economies. But it could be argued that the correlation is due to the reverse mechanism: there are innate productivity advantages in some places that lead to higher wages. Those higher wages attract more workers into the city, and make it even larger. In reality, both mechanisms are probably at play and wages and city size are simultaneously determined. A similar issue is at play for rents, since cities where rents are higher would be less attractive to households which should lead them to be smaller. This is accentuated by the fact that city size itself could be

13 perceived by households as an amenity, which introduces another source of endogeneity. We try to control for those issues by using control variables in our regression. We include the share of high-skilled workers in both our rent and wages regression. In the rent equation, we also include income, which should affect the demand for housing, and geographic information which could either make building more difficult (slope, maximum altitude), traduce a specific housing market effect (dummies for sharing a border with another country), or make cities more attractive, increasing both housing price and population (proximity to a body of water). There are other potential ways to circumvent those issues that have been used in the literature. For instance one could using panel data and run regressions that include city fixed effects as well as characteristics of the housing (size, distance to the centre, type...) in the rent equation(Albouy, 2008, Combes, Duranton, et al., 2012). For the wage equation, one could add individual fixed effects or characteristics (age, race, gender, education...), and possibly industry fixed effects (Albouy, 2008, Albouy and Lue, 2015, Combes, Duranton, et al., 2008). The city fixed effects would then measure an index of wage and housing in each city, net of all other controlled characteristics. It would also be possible to instrument city size with historical variables (Combes, Duranton, et al., 2008), or geology (Rosenthal et al., 2008). But all those methods require data that was not available to us. Another empirical challenge was the potential presence of spatial auto-correlation due to omit- ted variable like market potential. This might be a problem particularly at the urban unit level: by definition, workers in two urban units within the same area share very similar employment and housing markets. This is the reason why, in our analysis at the urban unit level, we only consider urban units that are at the centre of an urban area. All other urban units are likely to share too many characteristics with their neighbour, which would induce auto-correlation. Finally, the quality of our housing price data is not perfect. First, because there is almost no information on housing characteristics we cannot control for housing quality at all. This could bias the estimates of quality of life if some cities offer housing of lesser quality on average. The lower prices due to lower quality would then be interpreted for a lower quality of life. Furthermore, the data is not corrected for distance to the city centre of each housing unit. Because housing prices decrease with distance to the centre, as demonstrated for the case of France by Combes, Duranton, et al. (2012), and because the land area of a city like Paris is much larger than for instance Grenoble, using the median of housing price underestimates the housing costs differences across cities. This also complicates the interpretation of the land area variable we use in some of our regressions. Because of the incompleteness of our data, land area will capture both the extensive margin effect of extending urban sprawl, and the fact that average distance from the centre is generally larger in more populated cities. Keeping in mind all those limitations will be important in the interpretation of our results in later stages.

4 First-step regressions: Wages and rent gradients

4.1 Rent estimates

A first necessary step towards computing quality of life estimates, is to obtain comparable estimates of housing prices across cities. To obtain this price index for a comparable household, we compute

14 housing prices net of the effect of education. To that end, we estimate the equation

H P P P P ln pc = α + Xc β + µc (8)

H P where pc is the median price of old housing per square meter in city c, µc is the error term, and Xc is a set of controls for the city’s characteristics which include at least the natural logarithm of the city’s population, and some extra controls which are used to try to alleviate the endogeneity issues presented above. Table1 reports the results of several OLS regressions with various set of controls. Column 1 corresponds to a simple regression of housing prices on population, controlling for geography with maximum altitude and slope, dummies for being on the border with a neighbouring country, being on the coast of one of the main seas (British Channel, Mediterranean Sea, Atlantic Ocean) being on one of the 5 main rivers (Rhône, Garonne, Rhin, Seine, Loire). Column 2 controls for the log of median available income. Column 3 adds a control for the share of population with a higher education degree. Introducing those controls for the socio-economic composition of the city lowers the estimated coefficient on population, to the point that it becomes non-significant in column 3. This suggests that when the city is allowed to expand geographically, an increase in population keeping the same type socio-economic composition of the city does not affect housing prices.

Table 1: Housing price and city size, across Urban Area

Dependent variable: log median price of old housing per square meter Fringe adjustment Land area controlled (1) (2) (3) (4) (5) (6) ln Population 0.071∗∗∗ 0.037∗∗∗ −0.002 0.168∗∗∗ 0.150∗∗∗ 0.112∗∗∗ (0.010) (0.009) (0.010) (0.021) (0.019) (0.018)

ln Income 2.171∗∗∗ 1.252∗∗∗ 2.269∗∗∗ 1.348∗∗∗ (0.182) (0.209) (0.176) (0.201)

Education 3.453∗∗∗ 3.467∗∗∗ (0.439) (0.421)

ln Land area −0.109∗∗∗ −0.129∗∗∗ −0.130∗∗∗ (0.021) (0.019) (0.018)

Geography YYYYYY Observations 608 608 608 608 608 608 R2 0.427 0.589 0.602 0.464 0.630 0.647 Adjusted R2 0.413 0.578 0.591 0.451 0.620 0.636 Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01 Housing price of an Urban Area corresponds to the mean of the housing prices of the Urban Units within the area, weighted by population. Controlling for geography as slope and max altitude, as well as dummies for France’s neighbouring countries, seas, oceans and main rivers.

However in the case of France, where land use policies try to limit the spatial spread of cities, it is most relevant to think about the case where the boundaries of the city are fixed. This is what we do in columns 4 to 6, which repeat the previous pattern now controlling for the log land area of the city. The strong negative effect of land area on housing prices can be explained by the fact

15 that it captures both the average distance of housing units to the city centre, and the extensive margin effect: by allowing land area to increase for a given population, the supply of land increases and the prices decrease. The same extensive margin reasoning explains why the estimated population elasticity of hous- ing prices is much higher when we do not allow for land area to adjust. In columns 1 to 3, an increase in population had two opposite effects. First, density could increase leading to a higher demand for housing and an increase in prices. But in the medium to long-run the supply of land could increase through an expansion of the city, leading to a relative decrease in prices, and atten- uating the first effect. In the second part of the table however, an increase in population can only mean an increase in housing density which means a rise in price. Our preferred specification is that of column 6 which controls for both the composition of the city and its land area. It yields an estimate of 0.112 for the population elasticity. This is significantly smaller than the elasticity of 0.208 found by Combes, Duranton, et al. (2012), but can be explained by the fact that their measure of prices at the centre of cities captures higher differences in prices across cities than the median of the urban area we use. We will later use this column 6 to render the housing prices net of the education effect.

4.2 Wages and income

To compare the situation of similar workers in different cities, we also need to estimate the rela- tionship of wages with city size and education. We regress first wages on density, with the following equation:

w w w w ln wc = α + Xc β + µc (9)

w where Wc is the mean hourly wage in city c, µc is the error term, and Xc corresponds to a set of city characteristics, including at least the natural logarithm of density or population. In a first regression, we use density of population as the main explanatory variable of equation 9, and add controls for education, land area, or both. Results are reported in Table2.

The advantage of controlling for both density and land area is that it allows us to really distinguish the extensive and intensive margin of city size. The coefficient on density is much larger than that on land area, by a factor of two in column 3 to four in column 4, when controlling for education. This result implies that an increase in population which goes through a higher density (keeping land area constant) would have a much higher effect on wages than an increase where the city expands but density doesn’t change. The density elasticity of wage is relatively stable across the specifications, around 3.5%. This result is in line with the previous estimate of 3.7% obtained by Combes, Duranton, et al. (2008). In table3 we report the results of a series of OLS regressions with the natural logarithm of population as an explanatory variable, instead of density. The elasticity of wages with respect to population is this time very sensitive to whether or not we include land area. Figure4 in AppendixA represents graphically the results of this table on a scatterplot of wages on population. The coefficient on the logarithm of land area, which is now negative, can be explained by

16 Table 2: Wage and density across Urban Areas

Dependent variable: ln Mean hourly wage (1) (2) (3) (4) ln Density 0.036∗∗∗ 0.030∗∗∗ 0.044∗∗∗ 0.034∗∗∗ (0.004) (0.003) (0.004) (0.003)

Education 1.002∗∗∗ 0.860∗∗∗ (0.051) (0.061)

ln Land Area 0.023∗∗∗ 0.008∗∗∗ (0.002) (0.002)

Observations 759 759 759 759 R2 0.104 0.409 0.269 0.423 Adjusted R2 0.103 0.408 0.267 0.420 Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01 the fact that when the city expands, keeping population constant, the density will mechanically decrease. As seen in table2, such a decrease in density would lead to a decrease in wage, probably through lesser agglomeration gains.

Table 3: Wage and city size (across Urban Area)

Dependent variable: ln Mean hourly wage Fringe adjustment Land area controlled (1) (2) (3) (4) ln Population 0.026∗∗∗ 0.013∗∗∗ 0.044∗∗∗ 0.034∗∗∗ (0.002) (0.002) (0.004) (0.003)

Education 0.806∗∗∗ 0.860∗∗∗ (0.063) (0.061)

ln Land area −0.021∗∗∗ −0.026∗∗∗ (0.004) (0.003)

Observations 759 759 759 759 R2 0.239 0.375 0.269 0.423 Adjusted R2 0.238 0.373 0.267 0.420 Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01

Whether we use density or population as an explanatory variable, education keeps a strong explanatory power. Out of our independent variables, it is the one that has the strongest effect on wages. This result seems intuitive, since we should expect skills to be a primary determinant of wages, and it confirms the importance of computing wages net of education in our quality of life index. This will be done using the results of column 4 since, as argued before, keeping land area constant is the most relevant way to model French urban policies.

But our model is one of household location choice. While wage should provide interesting

17 insights into the determinants of a individual worker’s choice of a place of work, it could be expected that households as a whole take more than wage levels into account when deciding where to live. A family making a decision on their residence would probably consider the total income they would earn, including some city-dependent elements other than wages (the unemployment rate or local taxation for instance). For this reason, we now estimate again equation (9) with available income per consumption unit as the dependent variable. The measure of available income we use includes all income (work and non-work related) and already deduces all direct taxes. It should hence be a good measure of what people consider in their location decision. The results are reported in table4.

Table 4: Available income and city size (across Urban Area)

Dependent variable: ln Median available income Fringe adjustment Land area controlled (1) (2) (3) (4) log Population 0.016∗∗∗ −0.006∗∗∗ 0.007 −0.008∗∗ (0.002) (0.002) (0.004) (0.003)

Education 1.302∗∗∗ 1.296∗∗∗ (0.061) (0.061)

log Land area 0.011∗∗ 0.003 (0.004) (0.003)

Observations 760 760 760 760 R2 0.083 0.428 0.090 0.429 Adjusted R2 0.082 0.427 0.088 0.427 Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01

The effect of population on revenue is not so clear anymore when considering income instead of wages. This could come from several channels. First, our measure of income is available income per unit of consumption. This means that the composition of households could be a missing variable whose absence biases the estimate. Indeed, city size and household composition are likely to be correlated, but their relationship is not an obvious one. On the first hand, larger cities are more expensive (as seen in table1 for the price of housing). As a result, families with similar socio-economic characteristics (income, education, age) should tend to have less children. This would imply that available income per unit of consumption should be larger in large cities, since there would be less units per households. On the other hand, larger cities are also more productive and offer higher wages. This means that a couple with similar education would actually earn more, and hence would tend to have more children. This would bias our estimate in the opposite direction. It is therefore difficult to predict whether our estimates are biased upward or downward before further work is done on the relationship between city size and household composition. But there are other variables that are missing and could be correlated with both population and available income. The composition of the city could be very important. For instance, one could argue that small cities are more likely to have a high share of retirees, who do not earn much

18 money, or a higher unemployment rate, which would also decrease available income. Given our very limited set of controls, there are a number of reasons that could explain why our estimates of the population elasticity of available income are so sensitive to the specification chosen. However, the share of population with a higher education degree is remarkably stable, and is in both columns 2 and 4 strongly positive and significant. The effect is even stronger than in our previous wage regressions. Hence, despite the complex relation of available income and population, we still use the results of column 4 to compute a measure of median income net of education in further sections.

4.3 On the way to expected wages: unemployment and tax rate

Equation (7) requires the computation of inter-urban expected wage differentials. In order to compare similar workers in every cities we want to control for the effect of skills, measured by education, on the expected wage. We have already done the necessary regression for wages, but we still need to measure the two other elements of expected wage (unemployment and tax rates) net of education as well. Thus, we regress the unemployment rate, computed as the number of unemployed people over the number of persons in the labour force, on education, land area and quadratic and cubic terms for the log of population, according to the equation:

u u u 2 u 3 u u u uc = α + γc ln Nc + δc (ln Nc) + ηc (ln Nc) + Xc β + µc (10)

u where Nc is the population of city c, Xc is a set of controls including land area and education, u and µc is the error term. Results are reported in table5. Quadratic and cubic terms are introduced progressively, in columns 2 and 3, then 5 and 6. The table suggests that the relationship between unemployment and log population is concave over our range of population, and decreasing at least after a threshold. The coefficient on education is remarkably stable, whether we include land area or not, and whatever the degree of the popu- lation polynomial. This is reassuring for the next step of the analysis where we use this estimate to compute an unemployment rate net of education. To do this, we use the results of column 6, which seems to be the specification that best fits the case where land area is controlled.

We perform the same analysis on tax rate, estimating an equation of the form:

τ τ τ τ τc = α + Xc β + µc (11)

τ where τc is the tax rate in city c, and Xc corresponds to city characteristics, including the natural logarithm of population, education and the natural logarithm of declared income per unit τ of consumption (before tax deduction). µc is the error term. We chose not to include land area as a control, since it did not seem obvious that the tax rate in a city would depend on its spread, especially once income is controlled for. We include population to control for the possibility that larger cities provide more publicly funded amenities (cultural or transport ones for instance), which could be reflected in the local tax rate for a given income. This possibility is not confirmed in our results, since population loses significance as soon as controls for

19 Table 5: Unemployment and city size across Urban Areas

Dependent variable: Unemployment rate Fringe adjustment Land area controlled (1) (2) (3) (4) (5) (6) log Population 0.009∗∗∗ 0.031∗∗∗ 0.178∗∗∗ 0.011∗∗∗ 0.016 0.408∗∗∗ (0.001) (0.010) (0.065) (0.001) (0.014) (0.081) square log Population −0.001∗∗ −0.015∗∗ −0.0003 −0.039∗∗∗ (0.0005) (0.006) (0.001) (0.008) cube log Population 0.0004∗∗ 0.001∗∗∗ (0.0002) (0.0003)

Land Area −0.0000∗∗∗ −0.0000 −0.0000∗∗∗ (0.0000) (0.0000) (0.0000)

Education −0.521∗∗∗ −0.520∗∗∗ −0.523∗∗∗ −0.515∗∗∗ −0.516∗∗∗ −0.511∗∗∗ (0.038) (0.038) (0.038) (0.038) (0.038) (0.037)

Observations 760 760 760 760 760 760 R2 0.201 0.206 0.212 0.209 0.209 0.233 Adjusted R2 0.199 0.203 0.208 0.205 0.205 0.228 Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01 skills and income are added in the regression in columns 2 and 3. However, it is still possible that the tax rate is larger in some cities due to a higher density of public amenities, even if those cities are not necessarily the largest ones. Since we want to find out the tax rate faced by a worker with a given education in computing our net tax rate, we need to estimate the effect of skills on taxes. When including only education in our equation, in column 2, we find that cities with a higher share of high-skilled workers have a significantly higher tax rate. However, this is likely to be due to educated workers earning higher wages. For this reason, we include in column 3 of the regression the median declared income in the city (before taxes). Even when controlling for income, we find that more educated cities have higher tax rates, which might be due to educated households highly valuing some sort of publicly provided amenity a lot and hence sorting themselves into cities that have higher tax rates but also higher amenities. We use the result of column 3 to compute the tax rate net of education.

20 Table 6: Tax rate and city size across urban areas

Dependent variable: Tax rate (1) (2) (3) log Population 0.004∗∗∗ 0.0002 0.0005 (0.0004) (0.0004) (0.0004)

Education 0.250∗∗∗ 0.167∗∗∗ (0.012) (0.015)

log income 0.050∗∗∗ (0.006)

Observations 759 759 759 R2 0.152 0.449 0.499 Adjusted R2 0.151 0.448 0.497 Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01

4.4 Is there a bell curve?

From all the regressions above, we compute log wages, income and rents, as well as unemployment rate and tax rate net of education. Those estimates are then used to test whether French urban areas exhibit the inverted U-shape relationship of net wage to city size first theorised by Henderson (1974). As seen in table3, wages increase with city size as a result of agglomeration economies. On the other hand, urban costs increase also with city size, as is represented in table1 for the specific case of housing costs. This increase in cost of living should be the factor that limits the expansion of cities. The assumption behind the idea of inverted U-shape curve is that wages increase faster than cost of living at first, until a population threshold is reached after which the relationship is inverted. Initially, as cities are small, agglomeration brings benefits through higher wages. Once the threshold is reached, the higher costs of living take the upper hand and further agglomeration results in net wage loss (net wage being here the wage received by households once living costs are deduced). This inverted U-shaped curve can only exist if either wages or rents have a non-linear relation- ship with population. Results of the regression of log housing costs and log wages on quadratic and cubic terms for population are presented in AppendixB. They suggest that while the hous- ing costs are linearly increasing with population (in log terms), mean hourly wages are increasing and slightly convex on the range of population of French cities. Obtaining a bell shaped curve is therefore theoretically possible. In order to evaluate the U-shape relationship, we need to weight down housing costs by their expenditure share. This is done to avoid overestimating the variation of urban costs with city size, since rents only represent a fraction of total cost of living, and we assumed earlier that the prices of non-housing goods did not vary across cities. In table7 are the results of a regression of log wages minus log housing costs on the square and cube of log population. We perform this regression with a share of housing that is constant across cities, and with the city size dependent share we computed earlier. We also do it controlling or not for land area, to distinguish the effect of density and of population increase on the net wage. Figure6 in AppendixB plots the net wage on the log of population. Both the plot and the table

21 seem to suggest a relationship that is at most log-linear and decreasing, but not concave. The log of population squared or cubed are never significant. The findings when using a variable share of housing in expenditure, even if interesting, are to a large extent due to the way computed this share of housing in expenditure in the first place. Because we did not use actual data, but simply computed a share that linearly increased with the log of population, we eliminated all variations not due to city size that might have been present in the raw data. The strong relationship between share of housing in expenditure and city size was forced by the way the share was computed. Hence, when we multiply housing prices by this share of housing in expenditure, we remove a large part of the variation in living costs, and further increase the difference in urban costs between small and large cities. This explains the strongly significant coefficient obtained in columns 3 and 7, the very high R2 in columns 3-4 and 7-8, and the much better fit in figures 6b and 6d of AppendixB. The analysis performed with this variable share is still interesting as an illustration of how the allocation of household’s expenditures would affect net wages and later quality of life estimates. But it is important to keep in mind this limitation whenever we use it, and to realise that our results might be a mechanical result of the relationship we impose. Nevertheless, our results could be the sign that cities in France are located on the decreasing half of the bell shaped curve, and are hence oversized.

Table 7: Bell curve: net wage and city size (Urban Areas)

Dependent variable:

ln(mean wage) − sw*ln(median housing price) Cst share (0.325) Variable share Cst share (0.325) Variable share (1) (2) (3) (4) (5) (6) (7) (8) ln Population 0.031 0.092 −0.299∗∗∗ −0.383 0.008 0.097 −0.307∗∗∗ −0.424 (0.042) (0.301) (0.061) (0.640) (0.043) (0.300) (0.062) (0.643)

Square ln Population −0.002 −0.007 −0.002 0.005 −0.001 −0.009 −0.001 0.008 (0.002) (0.027) (0.003) (0.050) (0.002) (0.027) (0.003) (0.051)

Cube ln Population 0.0002 −0.0002 0.0002 −0.0002 (0.001) (0.001) (0.001) (0.001)

Land Area controlled NNNNYYYY Observations 608 608 198 198 608 608 198 198 R2 0.002 0.002 0.973 0.973 0.010 0.010 0.973 0.973 Adjusted R2 -0.001 -0.003 0.973 0.973 0.005 0.004 0.973 0.972 Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01 Housing price of an Urban Area corresponds to the mean of the housing prices of the Urban Units within the area, weighted by population.

We computed the same regression on expected log wage, including unemployment and tax rate. Results are reported in table 19 of AppendixB. Again, the coefficients on log population are never significant when we use a constant share of housing in expenditure. With a variable share, we find a decreasing and slightly concave relationship between net expected log wage and the log city size.

22 5 Indexes of Quality of Life

5.1 Testing the parameters in the quality of life equation

The empirical estimation of equations (5) and (7) is extremely sensitive to the choice of parame- ters on rents and wages. Since it is impossible to perfectly recreate the relative importance that households put on wages and rents, it is up to the researcher to decide whether or not to include a variable, or how exactly to measure another. Albouy, 2008 for instance does not include un- employment in his index, but it might not be a negligible parameter in the French case. Endless discussions could be had on how to best parametrise the compensating differentials equations. We tried to justify our choice of parameters, but we will also check from our data whether or not they are plausible. By rearranging equations (5) and (7), we can express housing prices as a function of income or expected wages and quality of life:

ˆH ˆ s¯H pc =y ˆc + Qc ˆH ˆ ˆ s¯H pc =s ¯ww˜c + Qc

Under the perfect mobility assumption, these equation should hold for all cities. Therefore, if we could directly measure quality of life, a regression of housing costs on income should yield the correct parameter on yˆc and w˜ˆc. ˆH To test the validity of our parametrisation, we regress sH pc on our measure of available income. From the theory, we expect to obtain a value of 1. Column 1 of table8 reports the result of this simple OLS regression.

Table 8: Housing price and available income by Urban Areas

Dependent variable: 0.325 * differential housing price share housing *differential housing price (1) (2) (3) (4) (5) (6) differential available income 0.401∗∗∗ 0.610∗∗∗ 0.605∗∗∗ 0.123∗ 0.267∗∗∗ 0.280∗∗∗ (0.080) (0.067) (0.066) (0.065) (0.059) (0.060)

Natural amenities NYYNYY Artificial amenities NNYNNY Observations 608 606 606 198 198 198 R2 0.040 0.472 0.497 0.018 0.435 0.461 Adjusted R2 0.039 0.461 0.484 0.013 0.398 0.417 Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01 Rents and housing costs are net of education effects Artificial amenities include the number of universities, cinemas, and doctors per capita. Natural amenities include dummies for proximity to the sea or an ocean, as well as climate variables

The estimated coefficient of 0.4 does not correspond to our expectations. But this basic un- controlled regression suffers from an obvious endogeneity issue: the correct coefficient should only be obtained if we control for quality of life. In column 1, we completely ignore that variable. But since by assumption quality of life is correlated with both income and housing costs, not including it in the equation could be a major cause of bias. In particular, if quality of life is negatively correlated with income, which is a result of our model, then the estimated coefficient in column 1 will be biased downward. It is not possible to directly measure quality of life to include it as an

23 explanatory variable in the equation and eliminate this bias. Our best option is hence to control for amenities that we expect to be strong determinants of quality of life, in order to try to capture the effect of quality of life on housing cost. This is what we do in columns 2 and 3 of table8, introducing first natural amenities (dum- mies for location on sea or ocean front, climate variables, maximum altitude and slope) and then artificial ones (number of cinemas rooms, universities, and doctors per thousand). As expected, the introduction of amenities as explanatory variables significantly increases the estimate by 50% from 0.4 to 0.6. The R2 is also multiplied by 10, suggesting that quality of life does affect housing prices through amenities. It is interesting to note that artificial amenities have a much smaller explanatory power than natural ones, and do not significantly affect the estimated coefficient. This might be due to the fact that we use a very limited number of artificial amenities, which, on their own, might not have a very strong explanatory power on quality of life. Several reasons could explain why the estimate is significantly different from 1, even when introducing all controls. First, it is likely that our selection of amenities is incomplete, and does not measure the whole effect of quality of life on rents. Some quality of life elements are not observable, and we do not have data on others that could have been measured and might be relevant (number of restaurants or pollution levels for instance). Furthermore, the artificial amenities we include are highly endogenous: larger cities for instance might have more cinemas per capita, and also exhibit both higher rents and higher wages; people with higher income might sort into cities with more cultural offer...(explain). Finally, the coefficient on differential income should only be one if we assume that there is indeed perfect mobility, which might simply not be the case for reasons explained in section3. Repeating the same regressions with a variable share of housing in expenditures, we obtain results that are even further from our expectations. It is difficult to find a convincing explanation for this result, except for either a misspecification of our parameters (the share of housing in particular, which is obtained from an estimation and not actually observed), or a lack of appropriate controls for the quality of life. To check our assumptions on the parameters of equation (7), we perform the same pattern of regressions, using the differential of expected wages as an explanatory variable instead of the difference in available income. If our model is correct, we should find an estimate of approximately 0.53, which corresponds to the share of households’ income that comes from wages. Results are reported in table9. Again, our initial regression yields results that are lower than expected and even negative when no control is included. This negative coefficient suggests that the correlation between quality of life and expected wages is very negative, and stronger than the correlation between quality of life and available income. This result could be explained by the fact that our measure of available income includes a lot of elements that are not directly determined by quality of life (pensions, taxes, external income...), while wages should be more responsive to quality of life differences. Not including quality of life in our equation with expected wages should then lead to a stronger negative bias than with available income. When including controls for amenities in columns 2 and 3, the results are still significantly different from the value of 0.53 we should expect. This is probably due to the same issues described above, in particular the incompletness of our set of amenities. This time, repating the analysis for

24 Table 9: Housing price and expected wage by Urban Areas

Dependent variable: 0.325 * differential housing price share housing * differential housing price (1) (2) (3) (4) (5) (6) differential expected wage −0.137∗∗ 0.138∗∗∗ 0.146∗∗∗ −0.086 0.143∗∗ 0.162∗∗ (0.056) (0.050) (0.050) (0.063) (0.063) (0.063)

Natural amenities NYYNYY Artificial amenities NNYNNY Observations 608 606 606 198 198 198 R2 0.010 0.405 0.434 0.009 0.390 0.417 Adjusted R2 0.008 0.393 0.420 0.004 0.350 0.369 Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01 Rents and housing costs are net of education effects Artificial amenities include the number of universities, cinemas, and doctors per capita. Natural amenities include dummies for proximity to the sea or an ocean, as well as climate variables a variable share of housing leads to results that are not very different from the previous ones, and still significantly below our expected result of 0.53. Those results however, while not particularly encouraging, do not necessarily mean that our chosen parameters are wildly incorrect. It is still possible that by adding some relevant amenities and improving the way we control for quality of life we would obtain higher coefficients.

5.2 Quality of Life indexes

After this test our chosen parametrisation, and despite the remaining uncertainty about the cor- rectness of our parameters, we now turn to computing quality of life indexes. using equations (5) and (7). In all of our indexes, we choose to exclude the three cities that share a border with Switzerland and are outliers in terms of available income (Morteau, the French parts of the urban areas of Basel and Geneva). Those cities have the highest available income out of all the urban areas in our sample, but this is due to a labour market effect (proximity with Switzerland) and not to a lower quality of life. Because the housing market is also affected by this high income, we exclude those cities even in our index computed from expected wages.

Estimating quality of life from available income

H We first compute quality of life according to equation (5): Qcc =s ¯H pcc − ybc, with a constant share s¯H = 0.325. It would be cumbersome to report here the full results of the computation for the 605 urban areas of our sample, but the detailed table can be found in AppendixD. The 15 cities at the top and bottom of this index are reported in table 10. It is apparent that urban areas in southern France, where the weather is mild and the sea is near, are dominating the ranking together with urban areas in the mountain. At the bottom are found urban areas in more rural regions of France, with little natural amenities one could think of. This seems to be coherent with general expectations about quality of life in France. Figure1 allows us to better visualise the quality of life estimates. We plot the wages and housing prices differentials for all urban areas, with pˆc on the vertical axis and yˆc on the horizontal axis. The dotted blue line corresponds to the results of our preferred regression, column 3 in table

8. The solid line represents all the combinations of income and housing price such that Qˆc = 0, i.e.

25 Table 10: Quality of Life in Urban Areas, computed with income and constant share of housing

Qcc = 0.325 × housing − income

city Qcc housing income

1 Saint-Tropez 0.511 1.828 0.083 2 Chamonix-Mont-Blanc 0.401 1.158 −0.024 3 Sainte-Maxime 0.364 1.202 0.027 4 Bormes-les-Mimosas - Le Lavandou 0.358 1.248 0.048 5 Cavalaire-sur-Mer 0.340 1.147 0.033 6 La Flotte 0.328 1.193 0.060 7 Morzine 0.322 1.211 0.071 8 Menton - Monaco (partie française) 0.322 1.041 0.016 9 Le Grau-du-Roi 0.319 0.795 −0.061 10 Marseillan 0.317 0.751 −0.072 11 Cogolin 0.306 0.927 −0.005 12 Agde 0.303 0.667 −0.086 13 Fréjus 0.291 0.854 −0.013 14 Nice 0.285 0.759 −0.039 15 Saint-Cyprien 0.258 0.602 −0.062 ... 590 Vittel −0.186 −0.255 0.103 591 Commentry −0.188 −0.524 0.017 592 Beaumont-de-Lomagne −0.190 −0.583 0.0004 593 Thouars −0.191 −0.550 0.012 594 La Souterraine −0.195 −0.740 −0.045 595 Nogent −0.198 −0.587 0.007 596 Guéret −0.199 −0.621 −0.003 597 Gourin −0.199 −0.478 0.043 598 Pouzauges −0.199 −0.497 0.038 599 Mamers −0.201 −0.623 −0.002 600 Decazeville −0.209 −0.614 0.009 601 Mirecourt −0.230 −0.738 −0.010 602 Neufchâteau −0.240 −0.731 0.002 603 Clamecy −0.242 −0.753 −0.003 604 Aubusson −0.250 −1.041 −0.088 605 Gueugnon −0.259 −0.579 0.071 quality of life is at the level of the national average, according to our parameters. It corresponds H to the equation s¯H pˆc =y ˆc Cities above the solid line have a quality of life higher than average. The larger the distance between a city and the line, the higher the quality of life. The graph illustrates the fact that, even if our parametrisation is significantly different from the actual regression line, it does not affect very strongly the quality of life results. Very few urban areas are in-between the two lines and would be considered to have quality of life positive in our estimation but negative if we used the results from the regression of housing costs on income. The discrepancy happens mainly for cities whose expected wage much above or below the average. Most of the cities that are at the very top and bottom of the ranking would likely stay the same, even if we used the coefficients from our regression. Estimation of equation (5) using a variable share of housing, which only feasible for the 200 largest urban areas, yields a very close ranking. Once again, cities in Southern France, near the Mediterranean or Atlantic shore, score the highest, while urban areas at the bottom of the ranking are in central or North Eastern France. The 15 cities with the highest and lowest scores are reported in tables 11. To compare the results to those of table 10, one needs to keep in mind that the sample in the second table is much smaller, as it contains only 200 cities, out of which only 196 have all the data necessary to estimate a measure of quality of life. The fact that larger cities now

26 Table 11: Quality of Life in Urban Areas, computed with income and variable share of housing

Qcc = 0.325 × housing − income

City Qcc housing share income 1 Paris 0.258 0.661 0.394 0.002 2 Nice 0.225 0.709 0.273 −0.031 3 Marseille - Aix-en-Provence 0.171 0.418 0.299 −0.045 4 Beaucaire 0.166 0.141 0.105 −0.151 5 Montpellier 0.166 0.254 0.247 −0.103 6 Toulon 0.158 0.576 0.249 −0.015 7 Sète 0.146 0.479 0.158 −0.070 8 Arles 0.142 0.208 0.134 −0.114 9 Bayonne (partie française) 0.134 0.514 0.214 −0.025 10 Fréjus 0.134 0.804 0.160 −0.006 11 Narbonne 0.134 0.141 0.158 −0.111 12 Saint-Cyprien 0.127 0.553 0.131 −0.055 13 Avignon 0.126 0.233 0.241 −0.070 14 Menton - Monaco (partie française) 0.122 0.991 0.147 0.024 15 Berck 0.116 0.591 0.135 −0.037 ... 181 Châlons-en-Champagne −0.063 −0.162 0.152 0.039 182 Longwy (partie française) −0.067 −0.099 0.147 0.052 183 Thonon-les-Bains −0.067 0.534 0.157 0.151 184 Montceau-les-Mines −0.073 −0.415 0.124 0.022 185 Cluses −0.075 0.391 0.159 0.137 186 Flers −0.076 −0.519 0.122 0.012 187 Guéret −0.076 −0.671 0.107 0.004 188 Nevers −0.079 −0.395 0.162 0.015 189 Chaumont −0.081 −0.426 0.121 0.029 190 Bar-le-Duc −0.083 −0.462 0.109 0.032 191 Sarreguemines (partie française) −0.086 −0.394 0.124 0.037 192 Tulle −0.087 −0.556 0.106 0.028 193 Cognac −0.090 −0.239 0.127 0.060 194 Sarrebourg −0.093 −0.260 0.116 0.063 195 Montluçon −0.098 −0.578 0.150 0.011 196 Pontarlier −0.123 0.351 0.105 0.160

27 Figure 1: Quality of life: housing costs versus available income appear at the top of the ranking is partly due to the mechanical effect of removing from the sample the small urban areas that topped the first index. In reality, as shown in figure7 of AppendixC, when comparing the ranks of only the 200 largest cities under the two methods, the smaller cities are the ones that experience the biggest change in their ranking, and this change goes in both direction. However, it is true that for the 10 largest cities, using a variable share of housing in expenditures increases the estimated quality of life. This is an automatic result of the way we compute the share as an increasing function of population. This method inflates the measure of total cost of housing for larger cities and hence the quality of life estimate. It is this effect that pulls Paris to the 1st row of the table. This index is still interesting in that it provides insight into how quality of life indexes might underestimate the quality of life in big cities by ignoring one of the way through which households pay more to live in them. However it is constructed in a way that makes it a weaker measure than the one with constant share of housing. Because it relies on a computation rather than a measurement of the share of housing in expenditure, it removes all the unexplained variation in the actual data. This means that this estimation of quality of life is not actually measured from observations on income and housing costs, but also inferred from city size. We do not allow in our computations for the possibility that a large city could have a low share of housing in expenditure, or reversely. For small cities in particular, imposing a share of housing dependent on population seems to incur dramatic changes that make the index unreliable as a measure of quality of life, and more of a thought experiment.

28 An alternative index using expected wages

We now turn to estimation of equation (7), which allows us to compute quality of life from expected ˆ H ˆ wages rather than income : Qc =s ¯H pˆc − s¯ww˜c. The results of the first computation with a share of housing in expenditures constant across cities, and a share of wages in income of approximately 0.53 are reported in table 12. The results are remarkably stable compared to the estimation based on available income: 24 cities are present in both tables 10 and 12, and none of them moves from the top to the bottom or reversely. It is again apparent that cities in sunny areas or high in the mountains have strong quality of life advantages, while urban areas in central France fare less well.

Table 12: Quality of Life in Urban Areas, computed with wage and constant share of housing

Qcc = 0.325 × housing − 0.535 × expected wage

city Qˆc housing expected wage

1 Saint-Tropez 0.702 1.828 −0.201 2 Sainte-Maxime 0.500 1.202 −0.204 3 Bormes-les-Mimosas - Le Lavandou 0.476 1.248 −0.131 4 Cavalaire-sur-Mer 0.441 1.147 −0.127 5 La Flotte 0.435 1.193 −0.088 6 Ars-en-Ré 0.397 1.053 −0.101 7 Le Grau-du-Roi 0.396 0.795 −0.257 8 Agde 0.386 0.667 −0.316 9 Menton - Monaco (partie française) 0.368 1.041 −0.056 10 Morzine 0.363 1.211 0.057 11 Capbreton 0.363 0.708 −0.248 12 Chamonix-Mont-Blanc 0.353 1.158 0.044 13 Cogolin 0.352 0.927 −0.095 14 Quiberon 0.345 0.778 −0.171 15 Fréjus 0.344 0.854 −0.124 ... 590 Poligny −0.193 −0.568 0.015 591 Mirecourt −0.194 −0.738 −0.086 592 Beaumont-de-Lomagne −0.198 −0.583 0.017 593 Gourin −0.199 −0.478 0.081 594 Pouzauges −0.201 −0.497 0.073 595 Torigny-les-Villes −0.203 −0.301 0.197 596 Decazeville −0.205 −0.614 0.009 597 Guéret −0.205 −0.621 0.006 598 Tulle −0.208 −0.506 0.081 599 La Souterraine −0.208 −0.740 −0.060 600 Langeac −0.218 −0.807 −0.082 601 Neufchâteau −0.219 −0.731 −0.035 602 Clamecy −0.231 −0.753 −0.025 603 Nogent −0.242 −0.587 0.096 604 Gueugnon −0.297 −0.579 0.203 605 Aubusson −0.300 −1.041 −0.072

Figure2 draws our estimated housing cost differential on the expected wage differentials. As before, the solid red line corresponds to the combinations of rents and expected wages which lead to an average quality of life, according to our equation (7). The other two lines correspond to the result of columns 3 and of table ??. Finally, our last index of quality of life is based on expected wages differentials, and uses the variable share of housing in expenditures we have computed earlier. The best and worst ranked cities are reported in table 13. The results still seem coherent with general expectations about

29 Figure 2: Quality of life: housing costs versus expected wage quality of life in France, with cities on the shores over-represented in the top 15, and industrial or rural towns in the bottom part. As before, this new index inflates the quality of life estimated for very large cities, and has a more uncertain effect on smaller urban areas, as illustrated in Figure7 of appendixC. However, one needs again to keep in mind that this index is only computed for the largest 200 cities, for which we have been able to calculate a share of housing in expenditures. This means that smaller towns in the mountains for instance are automatically excluded, and that the large proportion of big cities in the table is partly due to this effect. As explained previously, this imposed relationship between city size and share of housing can be considered a weakness of the index. For this reason, our preferred index is still the one that uses a constant share of housing. However, we recognise that using the average share of housing is not a perfect specification either, as it erases a part of the variation in housing expenditures. It is likely that our quality of life estimates are biased downwards for large cities when using this constant share, since it underestimates actual housing expenditures of households. But since the whole model is defined in terms of deviation from the average, considering only the deviation in prices for a given average share of housing expenditures should still provide a good estimate of quality of life, without "forcing" a relationship with city size as we do when we compute the variable share of housing.

Our quality of life index seems not to be too sensitive to the choice of expected wages or available income as a measure of income levels which is is reassuring for the validity of our chosen parameters, and hence for the strength of our estimates. We verify whether this observation that the rankings

30 Table 13: Quality of Life in Urban Areas, computed with wage and variable share of housing

Qcc = share × housing − 0.535 × expected wage

city Qcc housing share expected wage 1 Paris 0.242 0.661 0.394 0.034 2 Nice 0.211 0.709 0.273 −0.034 3 Fréjus 0.185 0.804 0.160 −0.106 4 Toulon 0.168 0.576 0.249 −0.046 5 Menton - Monaco (partie française) 0.166 0.991 0.147 −0.039 6 Saint-Cyprien 0.154 0.553 0.131 −0.152 7 Marseille - Aix-en-Provence 0.149 0.418 0.299 −0.045 8 Bayonne (partie française) 0.139 0.514 0.214 −0.054 9 Montpellier 0.136 0.254 0.247 −0.137 10 Sète 0.126 0.479 0.158 −0.095 11 La Teste-de-Buch - Arcachon 0.124 0.629 0.141 −0.066 12 Bordeaux 0.119 0.390 0.281 −0.017 13 Berck 0.115 0.591 0.135 −0.065 14 Royan 0.108 0.503 0.128 −0.081 15 La Rochelle 0.104 0.457 0.198 −0.026 ... 181 Chalon-sur-Saône −0.069 −0.267 0.176 0.042 182 Saint-Lô −0.070 −0.229 0.130 0.075 183 Longwy (partie française) −0.070 −0.099 0.147 0.104 184 Nevers −0.070 −0.395 0.162 0.012 185 Cognac −0.072 −0.239 0.127 0.079 186 Lons-le-Saunier −0.074 −0.241 0.136 0.077 187 Le Creusot −0.077 −0.382 0.115 0.062 188 Montceau-les-Mines −0.080 −0.415 0.124 0.053 189 Niort −0.080 −0.201 0.183 0.080 190 Sarrebourg −0.083 −0.260 0.116 0.099 191 Dole −0.084 −0.133 0.141 0.121 192 Guéret −0.084 −0.671 0.107 0.023 193 Montluçon −0.087 −0.578 0.150 −0.0002 194 Chaumont −0.092 −0.426 0.121 0.076 195 Flers −0.100 −0.519 0.122 0.069 196 Tulle −0.112 −0.556 0.106 0.099 are stable is correct by computing the correlations between rankings in all four indexes, reported in table 14. The very high correlations seem to justify our choice of parameters and confirm that, when weighted correctly, available income and expected wages are broadly equivalent and both relevant to the study of households’ location choices. In particular, the correlation between rankings in our two preferred indexes (wage and income with constant share of housing in expenditures) is very high, at 0.961.

6 The determinants of Quality of Life

Based on theory of amenities by Rosen (1979) and Roback (1982) and following the method of Albouy (2008), we can now perform a second-step estimation to find out the valuation of certain amenities by households. The model is obtained from Albouy (2008). ˜ k Recall that we defined quality of life to be an index of amenities, of the form Qc = Q(Ac ). If 1 ∂E we observed all the relevant amenities, our quality of life estimate Qˆc = − dQc could then y¯ ∂Qc be expressed as a function of amenities which could be estimated by regression of the following

31 Table 14: Correlation matrix between QoL rankings (Urban Areas)

Income Wage Share: Variable Constant Variable Constant Income Variable 1 0.913 0.828 0.767 Constant − 1 0.867 0.961∗ Wage Variable − − 1 0.942 Constant − − − 1 Note: *This correlation was computed on the full sample of all urban areas. All other correlations are based on the subsample of 200 largest cities, because indexes based on variable shared of housing are only available for those 200 urban areas. equation:

ˆ X k k k Qc = π Ac + µ k

k 1 ∂E ∂Q˜ where π = − k represents the valuation of each amenity by households. y¯ ∂Qc ∂A But in reality, quality of life depends on a very high number of amenities, many of them unobservable. A simple OLS regression will then yield result that are likely to suffer from strong bias, and cannot be directly interpreted as the monetary valuation of an amenity. Nevertheless, such a regression could still be informative, and it would be reassuring if the coefficient on amenities at least had the sign that would be expected from general assumptions of quality of life. We perform this second-step regression using our two preferred indexes of quality of life: income and wages, with a constant share of housing expenditures. The reasons why these specifications seem stronger to us were already exposed above. Furthermore, using them allows us to perform our regression on the full sample of urban areas, and not only on the 200 largest cities. Working on the restricted sample could prove particularly particularly since it will exclude urban areas where land development is complicated by some external characteristic, which could also be correlated with quality of life: for instance most urban areas high in the mountain are not in the subsample of 200 largest cities. We control for two types of amenities: natural and artificial ones. Our natural amenities include climate variables that measure temperatures and precipitations in winter. We expect winter temperatures to have a positive coefficient, which would traduce preference for warmer winters. Rains should have a negative coefficient. We include the maximum altitude and slope as control for being in the mountain. In theory, we expect the maximum altitude to be attractive to households and have a positive effect on quality of life, while slope could have a negative effect due to the increased difficulty of living in such an area. But it could also be argued that altitude means colder temperatures and isolation, while slope signifies proximity to the mountains which is enough to improve quality of life. In that case the coefficients would be reversed. We include controls for geography in the form of dummies for sharing a border with a neigh- bouring country (Switzerland, Belgium, Luxembourg, Germany or Spain). While these dummies

32 are theoretically intended to capture labour or housing market effects, they are very likely to cap- ture other geographical characteristics (being in or close to the Alps for Switzerland for instance), and their coefficient is complicated to predict. We also control for proximity to the main bodies of water in France (Mediterranean Sea, Atlantic Ocean, and British Channel), in two different ways: distance to the shore, or dummy for being on the shore. The distance variable is likely to capture a lot of climatic characteristics. Distance to the Mediterrnanean Sea for instance could broadly be interpreted as proximity to southern France and its mild climate. The dummy on the other hand might be too restrictive: urban areas that do not have a direct access to the beach but are in close proximity to it might still benefit from it in their quality of life. Artificial amenities are more problematic to select and interpret, as they are highly endogenous. We chose to use three variables, for three types of amenities: the number of cinema rooms per thousand inhabitant for cultural amenities, the number of universities per thousand inhabitants for educational amenities, and the number of general practitioners for health related amenities. Our measure of universities does not only include public universités, but the number of higher education establishment in general (including business and engineering schools which are not considered universities in France). We fully acknowledge that this selection is likely to be too restricted, and that a lot of potentially measurable amenities would deserve to be included: criminality rates, number of restaurants and bar, air quality, density of the transport network, number of parks... The list of omitted variables is very long. We would have liked to be able to include more, but did not have access to the necessary data. However, we were also wary of including too many variables which might be collinear and decrease the precision of our estimates. Results of the second-step regression are reported in tables 15 (for the quality of life estimate based on income) and 16 (for the quality of life estimate based on expected wage). We first include the climatic and geographic characteristics of urban area alone, in column 1 of both tables. Rain and temperature are both significant and have the expected sign meaning that households do value areas with milder winter. Coefficients for slope and altitude are imprecise and non-significant, which probably translates the balance between enjoying the landscapes in the mountain, and being isolated from other cities. Those variables alone already explain 10 to 15% of the variance across urban areas. Artificial amenities, introduced on their own in column 2, have less explanatory power, and coefficients that are not all going in the expected direction. Cinemas and doctors per thousand both have the expected positive sign which implies that households value cultural offer and easy accessibility to health services. Universities however have a strong significant negative effect on our estimates of quality of life, which does not go well with our previous expectation that households should value easy access to education. But the result could be explained by the endogeneity of artificial amenities. It is possible that more skilled households sort into cities with more educa- tional offer, or that cities with highly skilled inhabitants value education more and create more universities. If unobserved skills are positively correlated with our imprecise measure of educa- tion, then such cities should have both higher available income (or higher expected wages) and more universities. Since a high income leads to a decrease in estimated quality of life, this could explain why educational facilities are negatively correlated with quality of life. Another potential

33 explanation could argue that urban areas where there is a large number of universities benefit from positive externalities of learning, with university students or graduates sharing the skills they learned with their coworkers, family or neighbours. This would again inflate available income and wages through unobserved skills, and lower the quality of life estimate. Combining climate and amenities in column 3 does not significantly change the findings on the valuation of those amenities. We then introduce purely geographical variables in columns 4 to 9: dummies for sharing a border with another country, and distance or dummies for being on the shore. The estimated valuation of distance to the main bodies of water is much less precise than the coefficients on the dummies for being on the shore. In general, distance to the shore only matters for the Atlantic (column 4 of table 16 is the only exception, with people valuing distance to the British Channel). Using distance also makes the winter rains become insignificant in columns 5 and 6 of both tables, which suggests that the distance variable indeed captures some climate characteristics. Our preferred explanatory variable is hence dummies for being on the shore, which have much stronger and clearer coefficients, and also have the advantage of having more than twice the ex- planatory power on variation in quality of life across cities. Using dummies show that people highly value close proximity to the shore, with a strong preference for the Mediterranean sea, followed by the Atlantic and the British Channel. The dummy for sharing a border with Switzerland is strongly positive and significant. This is probably due to proximity to the Alps, especially since the labour market effect of being near Switzerland should imply higher income, and hence lower quality of life. Except for Switzerland, when quality of life is computed from expected wages, sharing a border with another country does not significantly impact quality of life (columns 7 to 9 of table 16). Indeed, our measure of wages only concerns salaries from French firms and hence does not take into account the income of cross-border workers. This income from households living in France but working across the border is captured in the measure of quality of life from available income. This might explain the negative impact of sharing the border with Germany, in columns 7 to 9 of table 15, since the high income of cross- border workers would decrease the quality of life estimate. The negative coefficient could also simply capture the potential unatractiveness of the Rhine region. The positive coefficient on the Belgium/Luxembourg dummy is harder to explain. While wages in Belgium might not be much higher than in France, and cross-border workers might not bias the estimate so much, there are a large amount of people working in Luxembourg and living in France with the income they earn there. However, there are only 14 urban areas that share a border with Belgium and Luxembourg, and it is possible that they all have very positive amenities that we do not measure and that are hence captured in the coefficient for the dummy. Introducing geographical variables in the form of dummies changes our findings on climate and artificial amenities only marginally. Slope becomes significant in table 15, but has a weak effect on quality of life. Other variables keep their signs and their values do not experience dramatic changes. Overall, our findings suggest that households strongly value mild winter and proximity to the shore and the Alps, as well as cultural offer and access to health services. All coefficients have the "correct" sign and are reassuring towards the quality of our estimates of quality of life, except for

34 universities, whose obtained valuation might be explained by endogeneity issues.

35 Table 15: Predictive power of amenities on Quality of Life (computed from income)

Dependent variable: QoLd Distance Dummy (1) (2) (3) (4) (5) (6) (7) (8) (9) Maximum altitude 0.00003 0.00002 −0.00004 −0.00004 0.00000 −0.00001 (0.00004) (0.00004) (0.00004) (0.00004) (0.00004) (0.00004) Slope 0.0001∗ 0.0001∗∗ 0.0001∗∗∗ 0.0001∗∗∗ 0.0001∗∗ 0.0001∗∗ (0.00005) (0.00005) (0.00005) (0.00005) (0.00004) (0.00004) Rain, winter −0.001∗∗∗ −0.001∗∗∗ 0.0004 0.0003 −0.002∗∗∗ −0.002∗∗∗ (0.0003) (0.0003) (0.0004) (0.0004) (0.0003) (0.0003) Temperature, winter 0.019∗∗∗ 0.019∗∗∗ 0.036∗∗∗ 0.036∗∗∗ 0.009∗∗∗ 0.009∗∗∗ (0.003) (0.003) (0.003) (0.003) (0.003) (0.002)

Universities per thousand −0.209∗∗ −0.177∗∗ −0.107 −0.138∗ (0.090) (0.083) (0.076) (0.071) Cinemas per thousand 0.087∗∗ 0.084∗∗ 0.102∗∗∗ 0.088∗∗∗ (0.036) (0.034) (0.032) (0.030) Doctors per thousand 0.032∗∗∗ 0.028∗∗∗ 0.021∗∗∗ 0.024∗∗∗

36 (0.009) (0.009) (0.008) (0.007)

Dist. British Channel 0.00002 −0.00004 −0.00005 (0.0001) (0.0001) (0.0001) Dist. Mediterranean −0.0001 −0.0001 −0.0001 (0.0001) (0.0001) (0.0001) Dist. Atlantic 0.0001∗∗ 0.0003∗∗∗ 0.0003∗∗∗ (0.00003) (0.00004) (0.00004)

Dummy British Channel 0.058∗∗∗ 0.076∗∗∗ 0.081∗∗∗ (0.019) (0.018) (0.018) Dummy Mediterranean 0.283∗∗∗ 0.241∗∗∗ 0.243∗∗∗ (0.021) (0.021) (0.021) Dummy Atlantic 0.110∗∗∗ 0.140∗∗∗ 0.136∗∗∗ (0.015) (0.016) (0.016)

Dummy Switzerland 0.042 0.113∗∗∗ 0.090∗∗∗ 0.094∗∗∗ 0.102∗∗∗ 0.080∗∗∗ (0.036) (0.032) (0.032) (0.031) (0.031) (0.030) Dummy Belgium/Luxembourg 0.041 0.022 0.025 0.034 0.063∗∗ 0.068∗∗ (0.036) (0.032) (0.032) (0.031) (0.030) (0.029) Dummy Germany −0.086∗∗ −0.086∗∗ −0.077∗∗ −0.058∗ −0.073∗∗ −0.064∗∗ (0.041) (0.037) (0.037) (0.035) (0.033) (0.033) Dummy Spain 0.105∗∗ 0.094∗∗ 0.082∗∗ 0.068∗ 0.027 0.011 (0.043) (0.038) (0.038) (0.038) (0.035) (0.035)

R2 0.150 0.042 0.179 0.111 0.295 0.317 0.314 0.410 0.431 Adjusted R2 0.144 0.037 0.170 0.101 0.282 0.301 0.306 0.399 0.417 Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01 Table 16: Predictive power of amenities on Quality of Life (computed from expected wage)

Dependent variable: QoLd Distance Dummy (1) (2) (3) (4) (5) (6) (7) (8) (9) Maximum altitude 0.00005 0.00004 −0.00001 −0.00001 0.00001 0.00000 (0.00005) (0.00005) (0.00005) (0.00005) (0.00004) (0.00004) Slope 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 (0.0001) (0.0001) (0.0001) (0.0001) (0.00004) (0.00004) Rain, winter −0.001∗∗ −0.001∗∗∗ 0.0002 0.0001 −0.002∗∗∗ −0.002∗∗∗ (0.0003) (0.0003) (0.0004) (0.0004) (0.0003) (0.0003) Temperature, winter 0.017∗∗∗ 0.017∗∗∗ 0.038∗∗∗ 0.038∗∗∗ 0.005∗∗ 0.005∗∗ (0.003) (0.003) (0.004) (0.004) (0.003) (0.003)

Universities per thousand −0.319∗∗∗ −0.295∗∗∗ −0.193∗∗ −0.225∗∗∗ (0.097) (0.093) (0.084) (0.073) Cinemas per thousand 0.098∗∗ 0.096∗∗ 0.100∗∗∗ 0.086∗∗∗ (0.039) (0.038) (0.035) (0.031) Doctors per thousand 0.030∗∗∗ 0.026∗∗∗ 0.020∗∗ 0.021∗∗∗ 37 (0.010) (0.010) (0.009) (0.008)

Dist. British Channel 0.0002∗∗ 0.0002 0.0001 (0.0001) (0.0001) (0.0001) Dist. Mediterranean 0.0001 0.0001 0.0001 (0.0001) (0.0001) (0.0001) Dist. Atlantic 0.00002 0.0003∗∗∗ 0.0003∗∗∗ (0.00003) (0.00005) (0.00004)

Dummy British Channel 0.066∗∗∗ 0.086∗∗∗ 0.092∗∗∗ (0.019) (0.018) (0.018) Dummy Mediterranean 0.319∗∗∗ 0.290∗∗∗ 0.292∗∗∗ (0.021) (0.021) (0.021) Dummy Atlantic 0.166∗∗∗ 0.204∗∗∗ 0.199∗∗∗ (0.015) (0.017) (0.016)

Dummy Switzerland 0.143∗∗∗ 0.222∗∗∗ 0.198∗∗∗ 0.203∗∗∗ 0.205∗∗∗ 0.181∗∗∗ (0.039) (0.036) (0.036) (0.032) (0.031) (0.031) Dummy Belgium/Luxembourg −0.002 −0.024 −0.020 0.007 0.028 0.033 (0.040) (0.036) (0.035) (0.032) (0.030) (0.030) Dummy Germany −0.042 −0.049 −0.038 0.009 −0.014 −0.004 (0.045) (0.041) (0.041) (0.035) (0.034) (0.034) Dummy Spain 0.098∗∗ 0.092∗∗ 0.080∗ 0.055 0.024 0.007 (0.046) (0.042) (0.042) (0.038) (0.036) (0.036) R2 0.094 0.031 0.119 0.136 0.328 0.345 0.300 0.345 0.362 Adjusted R2 0.088 0.026 0.109 0.126 0.316 0.330 0.292 0.333 0.346 Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01 Conclusion

Computing a quality of life index, and estimating the valuation of amenities households necessarily involves many simplifications. While non-academic literature is brimming with such rankings of the best places to live, to study or to work, it is complicated to create a theory-grounded index that yields results coherent with the popular literature. This paper adapts the methodology of Albouy (2008) and applies it to French data. We find that using a direct measure of available income or computing an expected wage taking into account unemployment and taxes both produce plausible quality of life indexes, which are coherent with general notions on quality of life. Cities in Southern France or in close proximity to the mountains fare best, while urban areas in rural isolated regions rank lowest in our indexes. Our results seem to suggest that natural amenities are such as climate and geographical loca- tions are the strongest determinants of quality of life. Artificial amenities, while significant, do not seem to explain a large part of the variation in quality of life across cities. However this result might be due to endogeneity issues and could be improved by replicating the analysis with more complete data on amenities. On the way to computing those quality of life indexes, we obtained wages and rent gradients that were coherent with the previous literature on the subject. We also tried to estimate how net wages evolved with city size, and found a decreasing relationship which might be a sign pointing towards French cities being oversized. Further research on the subject would be needed to confirm that result. Overall, this paper is a first try at computing a quality of life index on French data using hedonic methods. It could be greatly improved by using more detailed data, particularly on housing prices for which we only have a very raw measure. The model could also be extended to examine household heterogeneity in observable character- istics such as education or life-cycle value differently wages, rents and amenities.

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40 A Visualisation of the wage and rent gradients

This appendix presents graphically the results of our regressions of rents, wages and income on population. The name of the cities in the top and bottom percentile in terms of rents (resp. wages and income) are represented on the graph.

Figure 3: Housing price and city size

Figure 4: Mean wage and city size

41 Figure 5: Available income an city size

The two lines in figure5 with control for education and for land area and education have such close coefficients that they are indistinguishable from each other on the graph.

42 B Further insights into the bell curve

This appendix is a complement to the bell curve analysis in section4. It provides evidence that while rents exhibit at most a log-linear relationship with city size, the relationship between log mean wage and log population is slightly convex.

Table 17: Quadratic and Cubic terms in the wage equation (Urban Areas)

Dependent variable: ln mean hourly wage Fringe adjustment Land area controlled (1) (2) (3) (4) (5) (6) log Population 0.013∗∗∗ −0.069∗∗∗ −0.031 0.034∗∗∗ −0.036∗∗ −0.004 (0.002) (0.017) (0.107) (0.003) (0.017) (0.103) square log Population 0.004∗∗∗ 0.0004 0.003∗∗∗ 0.0003 (0.001) (0.010) (0.001) (0.010) cube log Population 0.0001 0.0001 (0.0003) (0.0003) ln Land area −0.026∗∗∗ −0.025∗∗∗ −0.025∗∗∗ (0.003) (0.003) (0.003) Education 0.806∗∗∗ 0.801∗∗∗ 0.800∗∗∗ 0.860∗∗∗ 0.852∗∗∗ 0.852∗∗∗ (0.063) (0.062) (0.062) (0.061) (0.060) (0.060) Observations 759 759 759 759 759 759 R2 0.375 0.394 0.394 0.423 0.436 0.436 Adjusted R2 0.373 0.392 0.391 0.420 0.433 0.432 Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01

Table 18: Quadratic and Cubic terms in the housing price equation (Urban Areas)

Dependent variable: log Median price of old housing per square meter Fringe adjustment Land area controlled (1) (2) (3) (4) (5) (6) log Population 0.017∗ −0.124 0.896 0.156∗∗∗ 0.108 0.825 (0.010) (0.093) (0.676) (0.019) (0.092) (0.639) Square log Population 0.007 −0.086 0.002 −0.063 (0.004) (0.061) (0.004) (0.058) Cube log Population 0.003 0.002 (0.002) (0.002) log Land area −0.163∗∗∗ −0.162∗∗∗ −0.161∗∗∗ (0.019) (0.019) (0.019) log Income 2.407∗∗∗ 2.401∗∗∗ 2.411∗∗∗ 2.351∗∗∗ 2.350∗∗∗ 2.357∗∗∗ (0.249) (0.249) (0.249) (0.235) (0.235) (0.235) Education 2.138∗∗∗ 2.100∗∗∗ 2.075∗∗∗ 2.436∗∗∗ 2.421∗∗∗ 2.402∗∗∗ (0.486) (0.486) (0.486) (0.460) (0.461) (0.461) Geography YYYYYY Observations 608 608 608 608 608 608 R2 0.602 0.603 0.605 0.647 0.647 0.648 Adjusted R2 0.591 0.592 0.593 0.636 0.636 0.636 Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01 Housing price of an Urban Area corresponds to the mean of the housing prices of the Urban Units within the area, weighted by population. Controlling for geography as distance from France’s neighbouring countries, seas, oceans and main rivers.

Figure6 graphically represents the net wage and net expected wage per city on population. It illustrates both the slightly decreasing nature of the relationship, and the way using a variable share of housing removes a large portion of the variation from the data, for reasons presented in section4.

43 Figure 6: Bell curve: graphic representation

(a) Wage and constant share of housing in expendi- (b) Wage and variable share of housing in expendi- tures tures (200 largest urban areas)

(c) Expected wage and constant share of housing in (d) Expected wage and variable share of housing in expenditures expenditures (200 largest urban areas)

Finally, table 19 presents evidence that using a variable share of housing in expenditure unveils a slightly concave relationship between net expected log wages and log population.

44 Table 19: Bell curve: net expected wage and city size (Urban Areas)

Dependent variable:

(1-tax)(1-unempl.)*ln(mean wage) − sw*ln(median housing price) Cst share (0.325) Variable share Cst share (0.325) Variable share

(1) (2) (3) (4) (5) (6) (7) (8) ln Population 0.027 −0.411 −0.199∗∗ −0.522 −0.059 −0.392 −0.263∗∗∗ −0.868 (0.051) (0.371) (0.080) (0.830) (0.051) (0.357) (0.075) (0.770)

Square ln Population −0.002 0.037 −0.007∗∗ 0.019 −0.001 0.029 −0.006∗ 0.042 (0.002) (0.033) (0.003) (0.065) (0.002) (0.032) (0.003) (0.061)

Cube ln Population −0.001 −0.001 −0.001 −0.001 (0.001) (0.002) (0.001) (0.002)

Land Area controlled NNNNYYYY

Observations 608 608 198 198 608 608 198 198 R2 0.055 0.058 0.962 0.962 0.125 0.127 0.967 0.967 Adjusted R2 0.052 0.053 0.961 0.961 0.121 0.121 0.967 0.967

Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01 Housing price of an Urban Area corresponds to the mean of the housing prices of the Urban Units within the area, weighted by population. Housing prices, wages, tax rate and unemployment are net of education.

45 C Quality of life: difference between rankings

This appendix complements the analysis in section5. It shows that using a variable or a constant share of housing incurs the most dramatic changes in ranking for the smaller cities in the panel, and that larger cities are only slightly advantaged by using a higher share of housing. A point being above the horizontal axis means that the city in question went up in the ranking when using the variable share of housing.

(a) Using available income (b) Using expected wage

Figure 7: Changes in the quality of life rankings, with constant or variable share of housing

46 D Quality of life: full rankings across Urban Areas

This appendix presents the quality of life ranking of all French urban areas for which we have data, according to the methodology developed in section5. Cities are ordered based on their ranking in the specification from income and with a constant share of housing in expenditure. The ranks in the specifications with the constant share of housing are out of 605. With a variable share of housing, 196 urban areas are ranked. Table 20: Quality of Life in Urban Areas

Constant share of housing Variable share of housing

city QoL: inc rank QoL: wage rank QoL: inc rank QoL: wage rank

Saint-Tropez 0.511 1 0.702 1 Chamonix-Mont-Blanc 0.401 2 0.353 12 Sainte-Maxime 0.364 3 0.500 2 Bormes-les-Mimosas - Le Lavandou 0.358 4 0.476 3 Cavalaire-sur-Mer 0.340 5 0.441 4 La Flotte 0.328 6 0.435 5 Morzine 0.322 7 0.363 10 Menton - Monaco (partie française) 0.322 8 0.368 9 0.122 14 0.166 5 Le Grau-du-Roi 0.319 9 0.396 7 Marseillan 0.317 10 0.343 16 Cogolin 0.306 11 0.352 13 Agde 0.303 12 0.386 8 Fréjus 0.291 13 0.344 15 0.134 10 0.185 3 Nice 0.285 14 0.274 24 0.225 2 0.211 2 Saint-Cyprien 0.258 15 0.287 23 0.127 12 0.154 6 Dives-sur-Mer 0.256 16 0.290 21 0.067 32 0.099 16 Aigues-Mortes 0.254 17 0.289 22 Capbreton 0.253 18 0.363 11 Port-la-Nouvelle 0.252 19 0.320 19 Berck 0.252 20 0.252 27 0.116 15 0.115 13 Noirmoutier-en-l’Île 0.251 21 0.328 17 Banyuls-sur-Mer 0.250 22 0.249 28 Sète 0.250 23 0.232 34 0.146 7 0.126 10 Ars-en-Ré 0.247 24 0.397 6 Uzès 0.246 25 0.221 37 L’Île-d’Yeu 0.241 26 0.325 18 Paris 0.237 27 0.222 35 0.258 1 0.242 1 Vaison-la-Romaine 0.237 28 0.198 43 Toulon 0.226 29 0.238 32 0.158 6 0.168 4 Saint-Rémy-de-Provence 0.225 30 0.191 50 Beaucaire 0.220 31 0.138 72 0.166 4 0.082 22 Carnac 0.217 32 0.313 20 Le Luc 0.216 33 0.241 29 Bayonne (partie française) 0.215 34 0.222 36 0.134 9 0.139 8 Montpellier 0.209 35 0.181 57 0.166 5 0.136 9 Abondance 0.208 36 0.264 26 Arles 0.205 37 0.121 83 0.142 8 0.055 36 Marseille - Aix-en-Provence 0.205 38 0.186 53 0.171 3 0.149 7 Brignoles 0.204 39 0.191 49 Pézenas 0.202 40 0.152 67 Nyons 0.201 41 0.219 39 Clermont-l’Hérault 0.199 42 0.128 80 Bourg-Saint-Maurice 0.197 43 0.153 66 Apt 0.195 44 0.192 47 Valréas 0.191 45 0.128 79 Creil 0.186 46 0.133 76 0.111 17 0.056 35 La Teste-de-Buch - Arcachon 0.186 47 0.265 25 0.046 43 0.124 11 Saint-Malo 0.183 48 0.192 48 0.068 30 0.075 25 Lunel 0.181 49 0.138 73 0.102 24 0.057 33 Narbonne 0.181 50 0.143 71 0.134 11 0.094 17 Samoëns 0.174 51 0.182 56 Draguignan 0.172 52 0.178 59 0.083 27 0.087 19 Thônes 0.170 53 0.185 54 Aime-la-Plagne 0.170 54 0.146 70 Briançon 0.170 55 0.077 130 Avignon 0.169 56 0.130 78 0.126 13 0.085 20 Sallanches 0.169 57 0.165 61 0.014 73 0.008 77 Saint-Brevin-les-Pins 0.167 58 0.197 44 La Rochelle 0.162 59 0.188 52 0.080 28 0.104 15 Embrun 0.161 60 0.123 81 Salernes 0.160 61 0.157 63 Noyon 0.160 62 0.132 77 Bollène 0.160 63 0.119 85 Ganges 0.156 64 0.113 90 Pornic 0.154 65 0.204 42 Forcalquier 0.154 66 0.105 94 Saint-Vincent-de-Tyrosse 0.151 67 0.179 58 Cadenet 0.151 68 0.084 122 Saint-Jean-de-Monts 0.150 69 0.239 30 Bordeaux 0.150 70 0.161 62 0.109 19 0.119 12 Barcelonnette 0.149 71 0.065 150 Crest 0.149 72 0.105 95 Mimizan 0.148 73 0.215 40

47 Table 20: Quality of Life in Urban Areas

Constant share of housing Variable share of housing

city QoL: inc rank QoL: wage rank QoL: inc rank QoL: wage rank

Nîmes 0.147 74 0.114 88 0.112 16 0.076 24 Quiberon 0.146 75 0.345 14 Les Sables-d’Olonne 0.145 76 0.207 41 0.019 67 0.078 23 Port-Saint-Louis-du-Rhône 0.142 77 0.095 107 Soustons 0.142 78 0.183 55 Béziers 0.141 79 0.088 118 0.111 18 0.056 34 Villard-de-Lans 0.140 80 0.101 102 Saint-Nazaire 0.139 81 0.151 69 0.061 34 0.071 27 Le Vigan 0.136 82 0.041 188 Salon-de-Provence 0.136 83 0.110 93 0.058 36 0.030 51 Lille (partie française) 0.136 84 0.097 105 0.107 20 0.065 30 Saint-Pierre-sur-Dives 0.136 85 0.151 68 Provins 0.134 86 0.122 82 Saint-Pierre-d’Oléron 0.134 87 0.238 31 Lyon 0.133 88 0.120 84 0.105 22 0.090 18 Perpignan 0.132 89 0.113 89 0.106 21 0.085 21 Alès 0.130 90 0.092 111 0.103 23 0.063 31 Bessan 0.130 91 0.070 142 Biscarrosse 0.129 92 0.219 38 Royan 0.129 93 0.232 33 0.006 84 0.108 14 Oraison 0.128 94 0.103 98 Boulogne-sur-Mer 0.127 95 0.104 96 0.091 25 0.065 29 Dinard 0.125 96 0.155 65 0.018 69 0.045 41 Manosque 0.120 97 0.083 124 0.068 31 0.029 52 Saint-Hilaire-de-Riez 0.119 98 0.192 46 Pithiviers 0.116 99 0.103 99 Douai - Lens 0.114 100 0.057 165 0.090 26 0.030 50 Lézignan-Corbières 0.113 101 0.060 159 Die 0.111 102 0.102 100 Dreux 0.111 103 0.094 109 0.054 39 0.035 47 Parentis-en-Born 0.111 104 0.134 75 Pierrelatte 0.109 105 0.057 164 Vernon 0.109 106 0.087 119 0.049 41 0.025 55 Annecy 0.106 107 0.165 60 0.009 78 0.066 28 Sisteron 0.104 108 0.037 193 Nantes 0.103 109 0.089 115 0.066 33 0.051 37 Beaurepaire 0.096 110 0.091 113 Honfleur 0.095 111 0.076 132 Calais 0.094 112 0.065 147 0.071 29 0.041 44 Auray 0.091 113 0.112 91 Céret 0.091 114 0.112 92 Bagnols-sur-Cèze 0.091 115 0.036 194 Prades 0.090 116 0.063 152 Reims 0.089 117 0.092 112 0.045 46 0.046 40 Aubenas 0.088 118 0.080 128 0.058 37 0.048 39 La Tremblade 0.085 119 0.156 64 Saint-Valery-en-Caux 0.081 120 0.032 196 Rennes 0.081 121 0.065 149 0.045 45 0.027 53 Gap 0.080 122 0.051 174 0.048 42 0.017 64 Montdidier 0.080 123 0.091 114 Vannes 0.079 124 0.099 104 0.032 56 0.049 38 Louviers 0.079 125 0.060 160 0.037 49 0.015 66 Bagnères-de-Luchon 0.079 126 0.050 175 Challans 0.078 127 0.096 106 Bellegarde-sur-Valserine 0.078 128 0.136 74 Doullens 0.078 129 0.076 135 Langon 0.077 130 0.062 154 Chambéry 0.076 131 0.079 129 0.023 62 0.023 56 Saint-Père-en-Retz 0.076 132 0.066 144 Amiens 0.075 133 0.073 137 0.039 48 0.036 46 Libourne 0.075 134 0.086 120 0.035 51 0.044 42 Compiègne 0.074 135 0.075 136 0.017 70 0.016 65 Amélie-les-Bains-Palalda 0.074 136 0.081 127 Toulouse 0.073 137 0.062 153 0.046 44 0.034 48 Sélestat 0.072 138 0.083 123 Abbeville 0.071 139 0.072 138 0.040 47 0.039 45 Saint-Omer 0.071 140 0.024 213 0.052 40 0.002 84 Avesnes-sur-Helpe 0.071 141 0.056 166 Yvetot 0.070 142 0.070 141 Strasbourg (partie française) 0.069 143 0.099 103 0.032 54 0.060 32 Falaise 0.068 144 0.049 177 Dieulefit 0.068 145 0.018 223 Valdahon 0.067 146 0.086 121 Bourg-Saint-Andéol 0.067 147 0.020 219 Laudun-l’Ardoise 0.067 148 −0.017 319 Dunkerque 0.066 149 0.041 186 0.032 55 0.005 79 Nogent-sur-Seine 0.066 150 −0.001 267 Feurs 0.065 151 0.032 199 Granville 0.064 152 0.088 117 −0.014 104 0.007 78 Fécamp 0.064 153 0.072 139 Valenciennes (partie française) 0.064 154 −0.003 274 0.061 35 −0.008 104 Ugine 0.064 155 0.008 241 Dol-de-Bretagne 0.064 156 0.045 181 Tours 0.063 157 0.058 161 0.027 60 0.020 61 Aiguillon 0.062 158 −0.007 281 Montélimar 0.062 159 0.032 197 0.035 50 0.003 83 Angers 0.061 160 0.054 170 0.030 57 0.021 58

48 Table 20: Quality of Life in Urban Areas

Constant share of housing Variable share of housing

city QoL: inc rank QoL: wage rank QoL: inc rank QoL: wage rank

Gaillac 0.060 161 0.022 216 Montauban 0.060 162 0.043 185 0.034 53 0.015 69 Joigny 0.059 163 0.027 207 Gérardmer 0.059 164 0.076 133 Lesparre-Médoc 0.058 165 0.104 97 Marennes 0.058 166 0.116 86 Caen 0.058 167 0.066 146 0.021 65 0.027 54 Saint-Just-en-Chaussée 0.057 168 0.076 134 Caudry 0.055 169 0.048 179 Faverges-Seythenex 0.055 170 0.065 148 Tarare 0.054 171 0.041 187 Bayeux 0.051 172 0.072 140 Rochefort 0.050 173 0.066 145 0.020 66 0.034 49 Pont-Saint-Esprit 0.050 174 −0.011 301 Thionville 0.050 175 0.038 190 0.009 79 −0.005 98 Grenoble 0.050 176 0.025 212 0.022 63 −0.005 97 Saint-Marcellin 0.049 177 0.016 228 Le Havre 0.049 178 0.060 158 0.007 83 0.015 67 Carentan les Marais 0.049 179 −0.018 320 Béthune 0.048 180 −0.005 279 0.028 59 −0.028 129 Romans-sur-Isère 0.048 181 0.020 221 0.028 58 −0.002 90 Caussade 0.047 182 0.028 203 Rouen 0.047 183 0.055 169 0.013 76 0.018 62 Vitré 0.047 184 0.028 205 −0.021 118 −0.043 152 Château-Arnoux-Saint-Auban 0.047 185 0.028 204 Thonon-les-Bains 0.046 186 0.189 51 −0.067 183 0.074 26 Armentières (partie française) 0.046 187 0.014 232 0.021 64 −0.013 113 Revel 0.046 188 0.007 245 Neufchâtel-en-Bray 0.046 189 0.061 155 Castillon-la-Bataille 0.045 190 −0.002 269 Castelsarrasin 0.045 191 −0.008 286 Bagnères-de-Bigorre 0.045 192 0.007 242 Dax 0.045 193 0.081 126 0.007 82 0.041 43 Ancenis 0.045 194 0.005 252 Boën 0.045 195 −0.009 290 Paimpol 0.044 196 0.053 171 Roye 0.044 197 0.077 131 Rethel 0.042 198 0.023 214 Miramont-de-Guyenne 0.042 199 0.032 198 Friville-Escarbotin 0.042 200 0.052 172 Beauvais 0.042 201 0.046 180 0.002 90 0.004 80 Machecoul-Saint-Même 0.041 202 0.031 200 Argelès-Gazost 0.041 203 0.003 258 Chartres 0.040 204 0.058 162 −0.017 110 −0.001 87 Senlis 0.039 205 0.067 143 Concarneau 0.039 206 0.083 125 Gamaches 0.039 207 0.043 184 Maubeuge (partie française) 0.039 208 −0.002 271 0.058 38 0.015 70 Albertville 0.039 209 0.021 218 −0.012 101 −0.033 137 Pauillac 0.039 210 0.049 178 Saint-Vaast-la-Hougue 0.038 211 0.058 163 Sarzeau 0.038 212 0.195 45 Beauvoir-sur-Mer 0.038 213 0.089 116 Vienne 0.037 214 0.020 222 −0.012 100 −0.032 136 Dijon 0.036 215 0.056 167 0.001 92 0.018 63 Fourmies 0.036 216 0.004 255 Lorient 0.035 217 0.050 176 0.002 89 0.015 68 La Mure 0.033 218 −0.002 270 Soissons 0.032 219 0.039 189 0.015 71 0.020 60 Besançon 0.030 220 0.017 225 0.013 75 −0.002 88 Lure 0.030 221 −0.014 310 Valence 0.029 222 0.011 238 0.014 72 −0.007 101 Troyes 0.027 223 0.044 183 0.007 81 0.021 57 La Voulte-sur-Rhône 0.026 224 0.003 259 Le Neubourg 0.026 225 0.061 157 La Réole 0.026 226 −0.035 353 Bédarieux 0.023 227 −0.002 272 Lavaur 0.022 228 −0.027 337 La Loupe 0.022 229 0.011 236 Saint-Paul-Trois-Châteaux 0.022 230 0.007 243 Verneuil-sur-Avre 0.021 231 0.0004 265 Orbec 0.021 232 −0.047 377 Hazebrouck 0.020 233 −0.011 300 Castelnaudary 0.020 234 −0.006 280 Pons 0.020 235 −0.008 288 Château-Thierry 0.019 236 0.037 192 −0.018 112 −0.002 93 Dieppe 0.017 237 0.006 251 −0.016 107 −0.029 133 Arras 0.017 238 0.011 237 0.004 85 −0.004 96 Gournay-en-Bray 0.017 239 0.028 206 Haguenau 0.017 240 0.064 151 −0.046 164 −0.001 86 Montbrison 0.016 241 −0.003 277 Belley 0.016 242 0.016 230 Les Herbiers 0.015 243 −0.003 275 Saint-Amand-les-Eaux 0.015 244 −0.033 349 0.014 74 −0.036 143 Metz 0.014 245 0.023 215 −0.010 98 −0.004 95 Thann - Cernay 0.013 246 0.045 182 −0.035 144 −0.006 99 Cluses 0.013 247 0.102 101 −0.075 185 0.011 72

49 Table 20: Quality of Life in Urban Areas

Constant share of housing Variable share of housing

city QoL: inc rank QoL: wage rank QoL: inc rank QoL: wage rank

Questembert 0.011 248 0.030 202 Semur-en-Auxois 0.011 249 −0.037 358 Saint-Seurin-sur-l’Isle 0.011 250 0.026 209 Saumur 0.011 251 0.002 262 0.009 80 −0.002 91 Beaune 0.010 252 0.017 227 −0.025 124 −0.020 119 Clermont-Ferrand 0.010 253 0.015 231 −0.015 105 −0.012 112 Toul 0.010 254 −0.023 329 Lisieux 0.009 255 0.004 254 −0.007 97 −0.013 114 Mont-de-Marsan 0.009 256 0.027 208 −0.014 102 0.003 82 Albi 0.008 257 0.017 226 0.003 87 0.010 73 Feuquières-en-Vimeu - Fressenneville 0.007 258 −0.009 292 Saintes 0.007 259 0.007 244 −0.001 94 −0.003 94 Les Andelys 0.006 260 0.031 201 Lannion 0.005 261 0.002 261 −0.005 96 −0.010 107 Bergerac 0.004 262 −0.011 298 0.010 77 −0.007 102 Beaupréau-en-Mauges 0.003 263 −0.038 359 Orléans 0.003 264 0.013 234 −0.023 121 −0.015 116 Évreux 0.003 265 0.008 240 −0.017 109 −0.014 115 La Roche-sur-Yon 0.002 266 −0.002 268 −0.014 103 −0.020 120 Mende 0.002 267 −0.011 299 Montreuil-Bellay 0.002 268 −0.014 309 Graulhet 0.002 269 −0.022 328 Hesdin 0.001 270 −0.003 276 Chauny −0.001 271 −0.014 312 Millau −0.001 272 −0.025 333 Forges-les-Eaux −0.001 273 0.006 250 Cherbourg-en-Cotentin −0.001 274 −0.016 314 −0.027 130 −0.044 154 Étain −0.002 275 −0.009 289 Salies-de-Béarn −0.002 276 −0.005 278 Montmirail −0.002 277 0.002 263 Limoux −0.003 278 −0.017 318 Lourdes −0.003 279 0.025 210 Péronne −0.003 280 0.014 233 Romilly-sur-Seine −0.004 281 0.021 217 Issoire −0.004 282 −0.007 283 Sens −0.004 283 0.025 211 −0.029 132 −0.002 89 Bernay −0.005 284 0.007 247 Saint-Vallier −0.006 285 −0.025 334 Tournon-sur-Rhône −0.006 286 −0.013 307 −0.016 108 −0.025 126 Agon-Coutainville −0.006 287 0.055 168 Pont-Audemer −0.006 288 −0.015 313 −0.034 142 −0.045 156 La Roche-Chalais - Saint-Aigulin −0.006 289 −0.044 373 Carcassonne −0.007 290 −0.036 354 0.034 52 0.004 81 Charleville-Mézières −0.007 291 −0.032 347 0.002 88 −0.024 123 Villeneuve-sur-Lot −0.007 292 −0.022 327 0.019 68 0.002 85 Saint-Pol-de-Léon −0.008 293 −0.010 296 Pont-l’Abbé −0.008 294 0.020 220 Vendôme −0.009 295 −0.009 294 −0.032 136 −0.035 142 Luçon −0.009 296 0.007 246 Nancy −0.010 297 0.004 256 −0.023 122 −0.012 109 Ham −0.010 298 0.003 260 Marckolsheim −0.010 299 0.094 110 La Bruffière −0.010 300 −0.031 345 Montaigu −0.011 301 −0.023 331 Lunéville −0.011 302 −0.019 322 Eu −0.012 303 0.00002 266 −0.044 159 −0.034 140 Châteaubriant −0.012 304 −0.049 383 Longué-Jumelles −0.013 305 −0.039 360 Plancoët −0.013 306 −0.013 306 Albert −0.014 307 −0.027 338 Doué-la-Fontaine −0.015 308 −0.009 291 Montargis −0.015 309 0.0004 264 −0.022 119 −0.008 105 Colmar −0.015 310 0.038 191 −0.043 158 0.008 75 Poitiers −0.016 311 −0.024 332 −0.018 113 −0.028 130 Saint-Hilaire-du-Harcouët −0.016 312 −0.054 399 Gannat −0.016 313 −0.045 375 Marmande −0.017 314 −0.031 346 −0.0001 93 −0.017 118 Le Mans −0.018 315 −0.023 330 −0.034 143 −0.042 149 Épernay −0.019 316 0.012 235 −0.036 147 −0.007 103 La Ferté-Bernard −0.019 317 −0.034 350 Modane −0.020 318 −0.079 458 Évron −0.020 319 −0.059 414 Soufflenheim −0.020 320 0.061 156 Lillebonne −0.020 321 −0.016 317 Commercy −0.021 322 −0.014 311 Castres −0.021 323 −0.044 370 −0.004 95 −0.029 131 Montpon-Ménestérol −0.021 324 −0.012 302 Rosporden −0.022 325 −0.032 348 Sablé-sur-Sarthe −0.022 326 −0.030 342 −0.040 156 −0.051 166 Pontarlier −0.023 327 0.115 87 −0.123 196 0.013 71 Baugé-en-Anjou −0.023 328 −0.068 444 Sedan −0.023 329 −0.026 335 0.026 61 0.021 59 Cholet −0.024 330 −0.036 356 −0.036 146 −0.050 165 Auxerre −0.025 331 −0.008 285 −0.040 154 −0.025 125 Coutances −0.026 332 −0.043 367 Laval −0.026 333 −0.057 410 −0.033 141 −0.066 178 Quimper −0.027 334 −0.019 323 −0.017 111 −0.012 110

50 Table 20: Quality of Life in Urban Areas

Constant share of housing Variable share of housing

city QoL: inc rank QoL: wage rank QoL: inc rank QoL: wage rank

Guebwiller −0.027 335 0.005 253 −0.035 145 −0.006 100 Solesmes −0.027 336 −0.016 315 Penmarch −0.027 337 0.016 229 Laon −0.028 338 −0.019 321 0.003 86 0.010 74 Loches −0.028 339 −0.013 304 Fougères −0.029 340 −0.055 402 −0.033 140 −0.062 175 Valognes −0.029 341 −0.066 435 Bourg-en-Bresse −0.029 342 −0.029 340 −0.046 165 −0.048 160 Lamballe −0.031 343 −0.042 363 Périgueux −0.031 344 −0.013 308 −0.027 129 −0.012 111 Montbéliard −0.031 345 −0.030 341 −0.036 149 −0.038 145 Vire Normandie −0.032 346 −0.056 404 −0.036 148 −0.062 176 Pau −0.032 347 −0.049 384 −0.032 135 −0.051 167 Chemillé-en-Anjou −0.032 348 −0.070 445 Migennes −0.033 349 −0.009 295 Saint-Florentin −0.033 350 0.003 257 Venarey-les-Laumes −0.033 351 −0.056 406 Tarascon-sur-Ariège −0.034 352 −0.088 481 Argentan −0.034 353 −0.008 287 Muzillac −0.034 354 −0.013 305 Malestroit −0.034 355 −0.052 388 Mourenx −0.035 356 −0.052 389 Agen −0.035 357 −0.049 382 −0.025 125 −0.041 148 Saint-Affrique −0.035 358 −0.059 415 Cambrai −0.035 359 −0.036 355 0.001 91 −0.002 92 Tréguier −0.036 360 −0.034 352 Ploërmel −0.036 361 −0.029 339 Blois −0.036 362 −0.031 344 −0.047 167 −0.043 153 Vic-en-Bigorre −0.037 363 −0.020 325 Saint-Dizier −0.037 364 −0.043 366 −0.020 115 −0.028 128 Loireauxence −0.037 365 −0.079 457 Delle (partie française) −0.037 366 0.052 173 Barbezieux-Saint-Hilaire −0.038 367 −0.073 451 Oyonnax −0.038 368 −0.053 392 −0.026 128 −0.043 151 Lamotte-Beuvron −0.038 369 −0.021 326 Dole −0.038 370 −0.083 464 −0.037 151 −0.084 191 Tournus −0.039 371 −0.043 365 Brive-la-Gaillarde −0.039 372 −0.068 441 −0.028 131 −0.059 172 Morcenx −0.039 373 −0.009 293 Brou −0.040 374 −0.003 273 Vic-Fezensac −0.040 375 −0.101 502 Saint-Étienne −0.041 376 −0.056 405 −0.046 163 −0.064 177 Douarnenez −0.041 377 −0.011 297 Crozon −0.041 378 −0.012 303 Château-Gontier −0.041 379 −0.078 455 Chantonnay −0.041 380 −0.072 450 Oloron-Sainte-Marie −0.042 381 −0.053 393 Belfort −0.042 382 −0.068 443 −0.020 116 −0.048 161 Chinon −0.042 383 −0.065 433 Dinan −0.042 384 −0.026 336 Avranches −0.043 385 −0.048 380 Contres −0.043 386 −0.020 324 Valence −0.043 387 −0.063 427 0.014 72 −0.007 101 Saint-Sever −0.044 388 −0.008 284 Beaumont-le-Roger −0.044 389 0.009 239 Le Puy-en-Velay −0.045 390 −0.068 442 −0.019 114 −0.045 155 Pont-à-Mousson −0.045 391 −0.061 419 Roanne −0.046 392 −0.054 395 −0.037 150 −0.046 157 Rodez −0.046 393 −0.067 439 −0.033 139 −0.056 170 Baud −0.046 394 −0.063 428 Le Cateau-Cambrésis −0.048 395 −0.087 476 Verdun −0.048 396 −0.050 385 −0.033 137 −0.037 144 Charlieu −0.049 397 −0.052 387 Saint-Brieuc −0.049 398 −0.044 369 −0.045 162 −0.042 150 Tergnier −0.049 399 −0.074 452 Surgères −0.049 400 0.007 248 Tonneins −0.050 401 −0.063 429 Brest −0.050 402 −0.041 361 −0.046 166 −0.039 147 Sarrebruck (ALL) - Forbach (partie française) −0.050 403 −0.044 371 −0.025 126 −0.021 121 Saint-Jean-d’Angély −0.050 404 −0.043 368 Tarbes −0.051 405 −0.054 394 −0.025 127 −0.030 135 Neuf-Brisach −0.051 406 −0.007 282 Creutzwald −0.053 407 −0.045 374 Pamiers −0.054 408 −0.056 408 −0.012 99 −0.016 117 Legé −0.054 409 −0.066 437 Chauvigny −0.054 410 −0.114 527 Mulhouse −0.055 411 0.018 224 −0.062 178 0.008 76 Alençon −0.055 412 −0.062 420 −0.039 152 −0.048 162 Vichy −0.055 413 −0.056 407 −0.030 133 −0.034 139 Auch −0.055 414 −0.064 431 −0.015 106 −0.026 127 Mauléon −0.055 415 −0.124 540 Saint-Quentin −0.055 416 −0.059 413 −0.024 123 −0.029 132 Mauges-sur-Loire −0.056 417 −0.112 523 Sainte-Sigolène −0.056 418 −0.047 379 Segré −0.057 419 −0.058 412 Redon −0.057 420 −0.058 411 Autun −0.057 421 −0.086 473

51 Table 20: Quality of Life in Urban Areas

Constant share of housing Variable share of housing

city QoL: inc rank QoL: wage rank QoL: inc rank QoL: wage rank

La Bresse −0.058 422 −0.072 449 Saint-Dié-des-Vosges −0.059 423 −0.044 372 −0.022 120 −0.009 106 Locminé −0.059 424 −0.063 430 Longwy (partie française) −0.061 425 −0.062 424 −0.067 182 −0.070 183 Château-du-Loir −0.061 426 −0.048 381 La Guerche-de-Bretagne −0.062 427 −0.084 467 Périers −0.063 428 −0.125 541 Saint-Lô −0.063 429 −0.089 483 −0.042 157 −0.070 182 Louhans −0.064 430 −0.076 453 Niort −0.064 431 −0.083 465 −0.059 174 −0.080 189 Mayenne −0.064 432 −0.072 448 Sézanne −0.065 433 −0.030 343 Limoges −0.065 434 −0.071 447 −0.053 171 −0.061 174 Bourgueil −0.065 435 −0.149 568 Quimperlé −0.065 436 −0.060 418 Bonneval −0.065 437 −0.037 357 Montréjeau −0.065 438 −0.054 396 Remiremont −0.066 439 −0.057 409 Cahors −0.067 440 −0.055 401 −0.021 117 −0.011 108 Lons-le-Saunier −0.067 441 −0.094 493 −0.045 161 −0.074 186 Pontivy −0.067 442 −0.034 351 Saint-Céré −0.068 443 −0.105 510 Saverne −0.068 444 −0.055 403 Ornans −0.068 445 −0.066 436 Châlons-en-Champagne −0.068 446 −0.041 362 −0.063 181 −0.038 146 Angoulême −0.069 447 −0.062 421 −0.055 173 −0.050 164 Aubigny-sur-Nère −0.069 448 −0.062 425 Bourges −0.069 449 −0.053 390 −0.061 176 −0.047 158 Courtenay −0.069 450 0.006 249 Champagnole −0.069 451 −0.066 438 Saint-Avold (partie française) −0.070 452 −0.060 416 −0.033 138 −0.024 124 Blaye −0.070 453 −0.115 528 Carmaux −0.070 454 −0.052 386 Sainte-Maure-de-Touraine −0.071 455 −0.087 477 Baume-les-Dames −0.071 456 −0.102 504 Châteauroux −0.075 457 −0.066 434 −0.061 177 −0.053 169 Figeac −0.076 458 −0.108 514 La Flèche −0.077 459 −0.064 432 Essarts en Bocage −0.077 460 −0.107 513 Vesoul −0.077 461 −0.084 468 −0.044 160 −0.053 168 Plouhinec - Audierne −0.078 462 −0.047 378 Parthenay −0.079 463 −0.093 489 Mortagne-sur-Sèvre −0.079 464 −0.094 491 Chalon-sur-Saône −0.079 465 −0.084 466 −0.063 180 −0.069 181 Châteaudun −0.080 466 −0.054 400 Nérac −0.080 467 −0.111 520 Sully-sur-Loire −0.084 468 −0.085 471 Luxeuil-les-Bains −0.084 469 −0.118 533 Varennes-sur-Allier −0.084 470 −0.086 474 Fleurance −0.084 471 −0.105 509 Orthez −0.084 472 −0.062 426 Descartes −0.085 473 −0.086 472 Châtellerault −0.085 474 −0.090 484 −0.063 179 −0.069 180 Brioude −0.085 475 −0.111 519 Vitry-le-François −0.086 476 −0.071 446 −0.047 168 −0.033 138 Hagetmau −0.087 477 −0.060 417 Reichshoffen - Niederbronn-les-Bains −0.087 478 −0.016 316 Moulins −0.087 479 −0.078 456 −0.053 172 −0.047 159 Villefranche-de-Rouergue −0.087 480 −0.090 486 Joinville −0.087 481 −0.106 512 Hirson −0.088 482 −0.131 549 Gien −0.088 483 −0.081 461 Selles-sur-Cher −0.089 484 −0.042 364 Mazamet −0.090 485 −0.095 496 Avallon −0.090 486 −0.099 499 Saint-Aignan −0.091 487 −0.081 463 Fleury-sur-Andelle −0.092 488 −0.053 391 Fontenay-le-Comte −0.093 489 −0.085 469 Saint-Junien −0.093 490 −0.102 506 Épinal −0.094 491 −0.089 482 −0.052 170 −0.049 163 Gourdon −0.095 492 −0.088 478 Arbois −0.096 493 −0.131 548 Salbris −0.097 494 −0.046 376 Argenton-sur-Creuse −0.098 495 −0.111 518 Bressuire −0.098 496 −0.116 530 Foix −0.098 497 −0.094 492 Châteaulin −0.098 498 −0.080 459 Langres −0.099 499 −0.091 488 Saint-Girons −0.099 500 −0.124 539 La Verrie −0.099 501 −0.128 542 Aire-sur-l’Adour −0.099 502 −0.108 515 Saint-Pourçain-sur-Sioule −0.099 503 −0.081 462 Mauléon-Licharre −0.099 504 −0.148 567 Nogent-le-Rotrou −0.100 505 −0.067 440 Bruyères −0.100 506 −0.103 508 Bogny-sur-Meuse −0.102 507 −0.090 487 Mortagne-au-Perche −0.102 508 −0.133 552

52 Table 20: Quality of Life in Urban Areas

Constant share of housing Variable share of housing

city QoL: inc rank QoL: wage rank QoL: inc rank QoL: wage rank

Revin −0.103 509 −0.130 546 Le Thillot −0.105 510 −0.088 480 Le Creusot −0.105 511 −0.131 550 −0.048 169 −0.077 187 Lalinde −0.105 512 −0.097 498 Montrichard −0.105 513 −0.054 397 Digoin −0.105 514 −0.116 532 Morlaix −0.106 515 −0.102 503 −0.032 134 −0.029 134 Saint-Maixent-l’École −0.106 516 −0.116 529 Aurillac −0.107 517 −0.113 524 −0.061 175 −0.068 179 Villedieu-les-Poêles-Rouffigny −0.108 518 −0.137 556 Carhaix-Plouguer −0.109 519 −0.103 507 Romorantin-Lanthenay −0.109 520 −0.090 485 Issoudun −0.110 521 −0.085 470 Saint-Jean-de-Maurienne −0.111 522 −0.145 564 Vierzon −0.112 523 −0.093 490 −0.039 153 −0.022 122 Loudéac −0.113 524 −0.116 531 Thiviers −0.113 525 −0.106 511 Cognac −0.114 526 −0.094 494 −0.090 193 −0.072 185 Lavelanet −0.114 527 −0.054 398 Saint-Pol-sur-Ternoise −0.115 528 −0.135 554 Saint-Laurent-sur-Sèvre −0.116 529 −0.164 575 Montbard −0.116 530 −0.100 501 Guer −0.117 531 −0.132 551 La Ferté-Macé −0.117 532 −0.146 565 Saint-Fulgent −0.117 533 −0.121 537 Paray-le-Monial −0.118 534 −0.120 536 Pontorson −0.119 535 −0.109 517 Nevers −0.120 536 −0.109 516 −0.079 188 −0.070 184 Guingamp −0.121 537 −0.129 543 Saint-Gaudens −0.121 538 −0.113 526 −0.040 155 −0.035 141 Cosne-Cours-sur-Loire −0.121 539 −0.088 479 Chauffailles −0.123 540 −0.145 563 Mirande −0.124 541 −0.121 538 Sarrebourg −0.124 542 −0.112 522 −0.093 194 −0.083 190 La Charité-sur-Loire −0.125 543 −0.099 500 Loudun −0.126 544 −0.112 521 Mussidan −0.127 545 −0.119 534 Ligny-en-Barrois −0.127 546 −0.080 460 Le Blanc −0.127 547 −0.152 570 Bar-sur-Aube −0.130 548 −0.078 454 Saint-James −0.131 549 −0.102 505 Saint-Amand-Montrond −0.131 550 −0.095 495 Jarny −0.132 551 −0.136 555 Condom −0.133 552 −0.163 574 Montceau-les-Mines −0.134 553 −0.138 558 −0.073 184 −0.080 188 Nueil-les-Aubiers −0.134 554 −0.187 586 Sancerre −0.137 555 −0.062 422 Brassac-les-Mines −0.137 556 −0.087 475 La Gacilly −0.139 557 −0.130 545 Condé-en-Normandie −0.140 558 −0.119 535 Lesneven −0.141 559 −0.152 569 Sarreguemines (partie française) −0.142 560 −0.113 525 −0.086 191 −0.059 173 Égletons −0.143 561 −0.175 581 Chaumont −0.144 562 −0.153 571 −0.081 189 −0.092 194 Maîche −0.144 563 0.095 108 Tonnerre −0.147 564 −0.143 561 Vouziers −0.148 565 −0.171 578 Raon-l’Étape −0.148 566 −0.062 423 Melle −0.151 567 −0.168 576 Poligny −0.154 568 −0.193 590 Hauts de Bienne −0.154 569 0.036 195 Domfront en Poiraie −0.154 570 −0.146 566 Châtillon-sur-Seine −0.155 571 −0.130 544 Flers −0.157 572 −0.180 583 −0.076 186 −0.100 195 Bar-le-Duc −0.159 573 −0.131 547 −0.083 190 −0.057 171 Pouancé −0.160 574 −0.134 553 Souillac −0.160 575 −0.143 560 Saint-Claude −0.162 576 −0.138 557 Torigny-les-Villes −0.164 577 −0.203 595 Saint-Yrieix-la-Perche −0.165 578 −0.170 577 Landivisiau −0.168 579 −0.153 572 Nontron −0.168 580 −0.140 559 Lannemezan −0.170 581 −0.173 580 Bellac −0.171 582 −0.173 579 Rostrenen −0.175 583 −0.190 587 Montluçon −0.176 584 −0.162 573 −0.098 195 −0.087 193 Pont-de-Buis-lès-Quimerch −0.179 585 −0.184 585 Decize −0.179 586 −0.143 562 Langeac −0.180 587 −0.218 600 La Châtre −0.184 588 −0.181 584 Tulle −0.185 589 −0.208 598 −0.087 192 −0.112 196 Vittel −0.186 590 −0.096 497 Commentry −0.188 591 −0.179 582 Beaumont-de-Lomagne −0.190 592 −0.198 592 Thouars −0.191 593 −0.193 589 La Souterraine −0.195 594 −0.208 599 Nogent −0.198 595 −0.242 603

53 Table 20: Quality of Life in Urban Areas

Constant share of housing Variable share of housing

city QoL: inc rank QoL: wage rank QoL: inc rank QoL: wage rank

Guéret −0.199 596 −0.205 597 −0.076 187 −0.084 192 Gourin −0.199 597 −0.199 593 Pouzauges −0.199 598 −0.201 594 Mamers −0.201 599 −0.191 588 Decazeville −0.209 600 −0.205 596 Mirecourt −0.230 601 −0.194 591 Neufchâteau −0.240 602 −0.219 601 Clamecy −0.242 603 −0.231 602 Aubusson −0.250 604 −0.300 605 Gueugnon −0.259 605 −0.297 604

54 E Results at the Urban Unit level

This appendix reproduces all the previous results, using data at the Urban Unit level. As explained in section2, this is the scale at which we obtained our housing prices estimates. As a result, our urban area prices only correspond to a mean of some of the urban units they contain, the ones where enough transactions happened. Because we are concerned that this discrepancy between the geographic scale of our rent information and the rest of our data might introduce some bias, we repeated all our estimations using the sample of urban units which are at the center of an urban area. Other non-central urban units are excluded to avoid spatial autocorrelation between our observations. Most of the results are unchanged when using this geographic scale. When there is some discrepancy with the urban area results we signal it and try to explain it. Tables are inserted in the same order as in the main part of our report.

First step regressions

Rent estimates

Table 21: Housing price and city size (across central Urban Units)

Dependent variable: ln Median price of old housing per square meter Fringe adjustment Land area controlled (1) (2) (3) (4) (5) (6) ln Population 0.095∗∗∗ 0.071∗∗∗ 0.028∗∗ 0.091∗∗∗ 0.081∗∗∗ 0.035∗∗ (0.010) (0.009) (0.011) (0.017) (0.015) (0.016)

ln Income 2.760∗∗∗ 2.752∗∗∗ (0.418) (0.418)

Education 2.146∗∗∗ 1.369∗∗∗ 2.161∗∗∗ 1.383∗∗∗ (0.171) (0.203) (0.172) (0.204)

ln Land area 0.008 −0.019 −0.015 (0.026) (0.023) (0.022)

Geography YYYYYY Observations 605 594 594 605 594 594 R2 0.481 0.592 0.621 0.481 0.593 0.621 Adjusted R2 0.468 0.581 0.610 0.467 0.581 0.609 Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01 Controlling for geography as slope and maximum altitude, as well as dummies for border with France’s neighbouring countries, seas, oceans and main rivers.

This first table on housing prices is one where using the urban unit level does incur some changes. Our estimation of the population elasticity is lower now, at 3.5% in the last column when it was 11.2% in table1 for Urban Areas. Furthermore, the land area is not significant anymore. This could be simply explained by the fact that by definition, central urban areas do not correspond to the actual city. The housing market of a city should be larger than its central

55 area. Hence the extensive margin explanation makes little sense here: extending the boundaries of a central urban unit should not significantly affect the prices since the housing market in which prices are determined is already larger than the urban unit. This would also explain why the population elasticity is not sensitive to whether we control for land area or not: even when we include land area, it does not actually correspond to the boundaries that would be pushed back to adjust to the higher demand for housing.

Wages and income

Table 22: Wage and density across Central Urban Units

Dependent variable: ln Mean hourly wage (1) (2) (3) (4) log density 0.039∗∗∗ 0.022∗∗∗ 0.033∗∗∗ 0.022∗∗∗ (0.003) (0.003) (0.003) (0.003)

Education 0.881∗∗∗ 0.810∗∗∗ (0.053) (0.062)

log Land Area 0.027∗∗∗ 0.007∗∗ (0.003) (0.003)

Observations 748 748 748 748 R2 0.167 0.391 0.256 0.395 Adjusted R2 0.166 0.389 0.254 0.393 Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01

Table 23: Wage and city size (across Urban Units central to an Urban Area)

Dependent variable: ln Mean hourly wage Fringe adjustment Land area controlled (1) (2) (3) (4) ln Population 0.030∗∗∗ 0.014∗∗∗ 0.033∗∗∗ 0.022∗∗∗ (0.002) (0.002) (0.003) (0.003)

Education 0.776∗∗∗ 0.810∗∗∗ (0.061) (0.062)

ln Land area −0.006 −0.015∗∗∗ (0.005) (0.004)

Observations 748 748 748 748 R2 0.254 0.385 0.256 0.395 Adjusted R2 0.253 0.383 0.254 0.393 Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01

56 Table 24: Available income and city size (across Urban Units central to a Urban Area)

Dependent variable: ln Median available income Fringe adjustment Land area controlled (1) (2) (3) (4) ln Population 0.011∗∗∗ −0.016∗∗∗ −0.001 −0.020∗∗∗ (0.002) (0.002) (0.004) (0.003)

Education 1.360∗∗∗ 1.343∗∗∗ (0.060) (0.061)

ln Land area 0.022∗∗∗ 0.007∗ (0.005) (0.004)

Observations 749 749 749 749 R2 0.033 0.425 0.055 0.428 Adjusted R2 0.032 0.424 0.053 0.425 Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01

The results for wages and income are very similar to the ones obtained for urban areas. Again, the elasticity of available income with respect to income is not clear, but the effect of education seems quite precisely estimated. We use the results of the last columns of each table to compute rents, wages and income net of the education effect.

Unemployment and tax rate

Table 25: Unemployment and city size across central Urban Units

Dependent variable: Unemployment rate Fringe adjustment Land area controlled (1) (2) (3) (4) (5) (6) log Population 0.016∗∗∗ 0.064∗∗∗ 0.138∗ 0.021∗∗∗ 0.030∗ 0.338∗∗∗ (0.001) (0.011) (0.078) (0.002) (0.015) (0.088) square log Population −0.002∗∗∗ −0.009 −0.0005 −0.030∗∗∗ (0.001) (0.007) (0.001) (0.008) cube log Population 0.0002 0.001∗∗∗ (0.0002) (0.0003)

Land Area −0.0000∗∗∗ −0.0000∗∗∗ −0.0000∗∗∗ (0.0000) (0.0000) (0.0000)

Education −0.559∗∗∗ −0.560∗∗∗ −0.561∗∗∗ −0.554∗∗∗ −0.555∗∗∗ −0.554∗∗∗ (0.037) (0.037) (0.037) (0.037) (0.037) (0.036)

Observations 760 760 760 760 760 760 R2 0.247 0.266 0.267 0.275 0.276 0.288 Adjusted R2 0.245 0.263 0.263 0.273 0.272 0.283 Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01

57 Table 26: Tax rate and city size across central urban units

Dependent variable: Tax rate (1) (2) (3) log Population 0.006∗∗∗ 0.001 0.001∗∗∗ (0.0004) (0.0004) (0.0004)

Education 0.252∗∗∗ 0.173∗∗∗ (0.012) (0.015)

log income 0.045∗∗∗ (0.006)

Observations 748 748 748 R2 0.192 0.492 0.532 Adjusted R2 0.190 0.491 0.530 Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01

Bell curve

Table 27: Bell curve: net wage and city size (central Urban Units)

Dependent variable:

*ln(mean wage) − sw*ln(median housing price) Cst share (0.325) Variable share Cst share (0.325) Variable share

(1) (2) (3) (4) (5) (6) (7) (8) ln Population −0.002 0.041 −0.292∗∗∗ −0.109 −0.001 0.047 −0.297∗∗∗ −0.263 (0.043) (0.314) (0.056) (0.580) (0.043) (0.310) (0.056) (0.579)

Square ln Population −0.0001 −0.004 −0.002 −0.016 0.001 −0.004 −0.001 −0.004 (0.002) (0.029) (0.002) (0.047) (0.002) (0.028) (0.002) (0.046)

Cube ln Population 0.0001 0.0004 0.0001 0.0001 (0.001) (0.001) (0.001) (0.001)

Land Area controlled NNNNYYYY Observations 598 598 199 199 598 598 199 199 R2 0.002 0.002 0.973 0.973 0.030 0.030 0.974 0.974 Adjusted R2 -0.002 -0.003 0.973 0.973 0.025 0.023 0.973 0.973 Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01

Index of quality of life

Regressions of rents on revenues

Quality of life from income Quality of life from expected wage

58 Table 28: Housing price and available income by central Urban Units

Dependent variable: 0.325 * differential housing price share housing * differential housing price (1) (2) (3) (4) (5) (6) differential available income 0.421∗∗∗ 0.506∗∗∗ 0.503∗∗∗ 0.203∗∗∗ 0.234∗∗∗ 0.230∗∗∗ (0.078) (0.066) (0.068) (0.065) (0.060) (0.064)

Natural amenities NYYNYY Artificial amenities NNYNNY Observations 598 594 594 199 199 199 R2 0.046 0.458 0.468 0.048 0.425 0.433 Adjusted R2 0.045 0.447 0.454 0.043 0.388 0.386 Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01 Rents and housing costs are net of education effects Artificial amenities include the number of universities, cinemas, and doctors per capita. Natural amenities include dummies for proximity to the sea or an ocean, as well as climate variables

Table 29: Housing price and expected wage by central Urban Units

Dependent variable: 0.325 * differential housing price share housing * differential housing price (1) (2) (3) (4) (5) (6) differential expected wage −0.028 0.160∗∗∗ 0.146∗∗∗ 0.069 0.152∗∗∗ 0.147∗∗∗ (0.055) (0.046) (0.048) (0.056) (0.049) (0.053)

Natural amenities NYYNYY Artificial amenities NNYNNY Observations 598 594 594 199 199 199 R2 0.0004 0.414 0.427 0.008 0.409 0.417 Adjusted R2 -0.001 0.402 0.412 0.003 0.371 0.369 Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01 Rents and housing costs are net of education effects Artificial amenities include the number of universities, cinemas, and doctors per capita. Natural amenities include dummies for proximity to the sea or an ocean, as well as climate variables

59 Table 30: Quality of Life in central Urban Units, computed with income and constant share of housing

Qcc = 0.325 × housing − income

City QoL housing income 1 Saint-Tropez 0.512 1.861 0.093 2 Chamonix-Mont-Blanc 0.414 1.226 −0.015 3 Sainte-Maxime 0.359 1.221 0.038 4 Bormes-les-Mimosas - Le Lavandou 0.345 1.246 0.060 5 Cavalaire-sur-Mer 0.334 1.165 0.044 6 Menton - Monaco (partie française) 0.328 1.093 0.027 7 Morzine 0.326 1.253 0.081 8 La Flotte 0.325 1.220 0.071 9 Le Grau-du-Roi 0.324 0.839 −0.051 10 Marseillan 0.299 0.738 −0.059 11 Nice 0.298 0.811 −0.035 12 Agde 0.291 0.669 −0.074 13 Fréjus 0.290 0.884 −0.002 14 Cogolin 0.285 0.905 0.009 15 Paris 0.284 0.801 −0.024 ... 580 Vittel −0.196 −0.245 0.116 581 Bellac −0.196 −0.607 −0.001 582 Decize −0.203 −0.462 0.053 583 Nogent −0.205 −0.607 0.008 584 Beaumont-de-Lomagne −0.211 −0.604 0.014 585 Mamers −0.213 −0.636 0.006 586 La Souterraine −0.213 −0.754 −0.032 587 Mirecourt −0.213 −0.717 −0.020 588 Aubusson −0.214 −1.036 −0.123 589 Clamecy −0.214 −0.814 −0.050 590 Pouzauges −0.214 −0.503 0.051 591 Commentry −0.214 −0.557 0.034 592 Neufchâteau −0.219 −0.746 −0.024 593 Gourin −0.222 −0.506 0.058 594 Decazeville −0.226 −0.629 0.021 595 Gueugnon −0.280 −0.607 0.083

Table 31: Quality of Life in central Urban Units, computed with income and variable share of housing

city QoL housing share income 1 Paris 0.303 0.794 0.386 0.004 2 Nice 0.224 0.804 0.270 −0.007 3 Montpellier 0.196 0.350 0.231 −0.116 4 Marseille - Aix-en-Provence 0.176 0.500 0.294 −0.029 5 Narbonne 0.156 0.207 0.131 −0.128 6 Toulon 0.151 0.661 0.245 0.011 7 Nîmes 0.149 0.159 0.191 −0.118 8 Béziers 0.147 −0.049 0.157 −0.155 9 Beaucaire 0.134 0.166 0.105 −0.117 10 Lyon 0.133 0.451 0.296 0.001 11 Lille (partie française) 0.131 0.246 0.274 −0.064 12 Bayonne (partie française) 0.130 0.618 0.203 −0.004 13 Strasbourg (partie française) 0.126 0.286 0.235 −0.059 14 Sète 0.123 0.536 0.158 −0.038 15 Avignon 0.120 0.309 0.234 −0.048 ... 182 Moulins −0.055 −0.263 0.116 0.025 183 Châteauroux −0.055 −0.211 0.139 0.026 184 Pont-à-Mousson −0.057 −0.116 0.094 0.046 185 Saint-Avold (partie française) −0.057 −0.245 0.111 0.030 186 Thann - Cernay −0.060 0.173 0.107 0.079 187 Cognac −0.064 −0.253 0.098 0.039 188 Guebwiller −0.064 0.006 0.103 0.065 189 Châtellerault −0.064 −0.228 0.119 0.037 190 Saint-Hilaire-de-Riez −0.065 0.584 0.096 0.121 191 Le Creusot −0.070 −0.339 0.109 0.033 192 Haguenau −0.070 0.253 0.137 0.105 193 Thonon-les-Bains −0.077 0.614 0.148 0.168 194 La Bresse −0.083 −0.102 0.094 0.073 195 Montceau-les-Mines −0.097 −0.393 0.117 0.051 196 Cluses −0.097 0.460 0.156 0.169 197 Montluçon −0.098 −0.529 0.135 0.026

60 Table 32: Quality of Life in central Urban Units, computed with wage and constant share of housing

Qcc = 0.325 × housing − 0.535 × expected wage

City QoL housing exp. wage 1 Saint-Tropez 0.700 1.861 −0.177 2 Sainte-Maxime 0.493 1.221 −0.180 3 Bormes-les-Mimosas - Le Lavandou 0.461 1.246 −0.105 4 Cavalaire-sur-Mer 0.433 1.165 −0.103 5 La Flotte 0.430 1.220 −0.063 6 Le Grau-du-Roi 0.399 0.839 −0.235 7 Ars-en-Ré 0.395 1.089 −0.077 8 Capbreton 0.381 0.796 −0.230 9 Menton - Monaco (partie française) 0.376 1.093 −0.039 10 Agde 0.373 0.669 −0.291 11 Chamonix-Mont-Blanc 0.366 1.226 0.061 12 Morzine 0.363 1.253 0.082 13 Fréjus 0.341 0.884 −0.100 14 Quiberon 0.333 0.784 −0.146 15 Cogolin 0.331 0.905 −0.068 ... 580 Clamecy −0.193 −0.814 −0.134 581 Pont-de-Buis-lès-Quimerch −0.197 −0.569 0.023 582 Tulle −0.197 −0.490 0.071 583 Bellac −0.198 −0.607 0.001 584 Commentry −0.200 −0.557 0.035 585 Rostrenen −0.203 −0.766 −0.087 586 Decazeville −0.211 −0.629 0.013 587 Nueil-les-Aubiers −0.215 −0.441 0.133 588 Pouzauges −0.217 −0.503 0.100 589 Beaumont-de-Lomagne −0.220 −0.604 0.044 590 Gourin −0.223 −0.506 0.109 591 Langeac −0.227 −0.791 −0.057 592 La Souterraine −0.227 −0.754 −0.034 593 Aubusson −0.246 −1.036 −0.169 594 Nogent −0.256 −0.607 0.110 595 Gueugnon −0.317 −0.607 0.224

Table 33: Quality of Life in central Urban Units, computed with wage and variable share of housing

Qcc = share × housing − 0.535 × expected wage

City QoL housing share exp. wage 1 Paris 0.275 0.794 0.386 0.058 2 Nice 0.213 0.804 0.270 0.007 3 Agde 0.194 0.662 0.097 −0.243 4 Fréjus 0.168 0.877 0.160 −0.052 5 Toulon 0.162 0.661 0.245 0.0001 6 Montpellier 0.160 0.350 0.231 −0.148 7 Menton - Monaco (partie française) 0.151 1.086 0.144 0.010 8 Marseille - Aix-en-Provence 0.150 0.500 0.294 −0.006 9 Bayonne (partie française) 0.139 0.618 0.203 −0.026 10 Saint-Cyprien 0.130 0.601 0.131 −0.096 11 Bordeaux 0.126 0.459 0.267 −0.007 12 La Rochelle 0.116 0.527 0.174 −0.045 13 Lyon 0.113 0.451 0.296 0.038 14 Strasbourg (partie française) 0.110 0.286 0.235 −0.081 15 Narbonne 0.110 0.207 0.131 −0.155 ... 182 Albertville −0.052 0.195 0.118 0.140 183 Mazamet −0.053 −0.386 0.096 0.030 184 Dole −0.056 −0.119 0.104 0.082 185 Cognac −0.056 −0.253 0.098 0.059 186 Hazebrouck −0.057 0.012 0.098 0.108 187 Saint-Amand-les-Eaux −0.057 −0.029 0.110 0.100 188 Fougères −0.058 −0.098 0.098 0.090 189 Brive-la-Gaillarde −0.058 −0.153 0.148 0.066 190 Chaumont −0.062 −0.417 0.093 0.043 191 Longwy (partie française) −0.068 −0.069 0.124 0.110 192 Saint-Étienne −0.068 −0.246 0.225 0.024 193 Pont-à-Mousson −0.072 −0.116 0.094 0.114 194 Montluçon −0.075 −0.529 0.135 0.008 195 Le Creusot −0.088 −0.339 0.109 0.095 196 La Bresse −0.096 −0.102 0.094 0.162 197 Montceau-les-Mines −0.097 −0.393 0.117 0.095

61 Table 34: Correlation matrix between QoL rankings (central Urban Units)

Income Wage Share: Variable Constant Variable Constant Income Variable 1 0.850 0.833 0.721 Constant − 1 0.865 0.953 Wage Variable − − 1 0.896 Constant − − − 1

62 Table 35: Predictive power of amenities on Quality of Life in central Urban Units (computed from income)

Dependent variable: QoLd Distance Dummy (1) (2) (3) (4) (5) (6) (7) (8) (9) Maximum altitude 0.00005 0.00004 −0.00002 −0.00003 0.00001 0.00000 (0.00004) (0.00004) (0.00004) (0.00004) (0.00003) (0.00003) Slope 0.0001 0.0001 0.0001∗∗ 0.0001∗∗ 0.0001∗ 0.0001∗ (0.00004) (0.00004) (0.00004) (0.00004) (0.00004) (0.00004) Rain, winter −0.001∗∗∗ −0.001∗∗∗ 0.001 0.0004 −0.002∗∗∗ −0.002∗∗∗ (0.0003) (0.0003) (0.0004) (0.0004) (0.0003) (0.0003) Temperature, winter 0.015∗∗∗ 0.016∗∗∗ 0.034∗∗∗ 0.035∗∗∗ 0.005∗∗ 0.006∗∗ (0.003) (0.003) (0.003) (0.003) (0.003) (0.003)

Universities per thousand −0.072 −0.045 0.045 0.024 (0.066) (0.064) (0.059) (0.056) Cinemas per thousand 0.041 0.056∗ 0.067∗∗ 0.061∗∗ (0.034) (0.033) (0.030) (0.029) Doctors per thousand 0.016∗ 0.017∗ 0.012 0.016∗∗ (0.009) (0.009) (0.008) (0.008) 63

Dist. British Channel 0.00001 −0.0001 −0.00004 (0.0001) (0.0001) (0.0001) Dist. Mediterranean −0.0001 −0.0001 −0.0001 (0.0001) (0.0001) (0.0001) Dist. Atlantic 0.0001∗∗∗ 0.0003∗∗∗ 0.0004∗∗∗ (0.00003) (0.00004) (0.00004)

Dummy British Channel 0.069∗∗∗ 0.087∗∗∗ 0.089∗∗∗ (0.021) (0.020) (0.020) Dummy Mediterranean 0.291∗∗∗ 0.259∗∗∗ 0.264∗∗∗ (0.023) (0.023) (0.023) Dummy Atlantic 0.104∗∗∗ 0.139∗∗∗ 0.140∗∗∗ (0.016) (0.018) (0.017)

Dummy Switzerland 0.071∗ 0.137∗∗∗ 0.126∗∗∗ 0.126∗∗∗ 0.120∗∗∗ 0.109∗∗∗ (0.039) (0.036) (0.036) (0.035) (0.034) (0.035) Dummy Belgium/Luxembourg 0.037 0.016 0.019 0.042 0.059∗ 0.064∗ (0.042) (0.037) (0.037) (0.037) (0.035) (0.035) Dummy Germany −0.070 −0.071∗ −0.067 −0.039 −0.054 −0.046 (0.045) (0.042) (0.042) (0.039) (0.038) (0.038) Dummy Spain 0.107∗∗ 0.115∗∗∗ 0.109∗∗∗ 0.063 0.047 0.037 (0.044) (0.040) (0.040) (0.040) (0.038) (0.038)

Observations 594 598 594 598 594 594 598 594 594 R2 0.115 0.010 0.126 0.115 0.290 0.302 0.272 0.347 0.358 Adjusted R2 0.109 0.005 0.116 0.105 0.277 0.285 0.263 0.334 0.343 Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01 Table 36: Predictive power of amenities on Quality of Life in central Urban Units (computed from wages)

Dependent variable: QoLd Distance Dummy (1) (2) (3) (4) (5) (6) (7) (8) (9) Maximum altitude 0.0001 0.0001 0.00001 0.00000 0.00002 0.00001 (0.00004) (0.00004) (0.00004) (0.00004) (0.00003) (0.00003) Slope 0.00002 0.00002 0.00005 0.0001 0.00004 0.00004 (0.00005) (0.00005) (0.00005) (0.00005) (0.00004) (0.00004) Rain, winter −0.001∗∗ −0.001∗∗ 0.0003 0.0002 −0.002∗∗∗ −0.002∗∗∗ (0.0003) (0.0003) (0.0004) (0.0004) (0.0003) (0.0003) Temperature, winter 0.015∗∗∗ 0.015∗∗∗ 0.035∗∗∗ 0.036∗∗∗ 0.003 0.004 (0.003) (0.003) (0.004) (0.004) (0.003) (0.003)

Universities per thousand −0.152∗∗ −0.125∗ −0.011 −0.023 (0.070) (0.070) (0.064) (0.056) Cinemas per thousand 0.052 0.065∗ 0.063∗ 0.058∗∗ (0.036) (0.036) (0.033) (0.029) Doctors per thousand 0.014 0.014 0.010 0.013∗

64 (0.010) (0.010) (0.009) (0.008)

Dist. British Channel 0.0002∗ 0.0001 0.0001 (0.0001) (0.0001) (0.0001) Dist. Mediterranean 0.0001 0.0001 0.0001 (0.0001) (0.0001) (0.0001) Dist. Atlantic 0.00003 0.0003∗∗∗ 0.0003∗∗∗ (0.00003) (0.00005) (0.00005)

Dummy British Channel 0.078∗∗∗ 0.098∗∗∗ 0.100∗∗∗ (0.021) (0.020) (0.020) Dummy Mediterranean 0.332∗∗∗ 0.309∗∗∗ 0.313∗∗∗ (0.023) (0.023) (0.023) Dummy Atlantic 0.163∗∗∗ 0.203∗∗∗ 0.203∗∗∗ (0.016) (0.017) (0.017) Dummy Switzerland 0.176∗∗∗ 0.251∗∗∗ 0.238∗∗∗ 0.235∗∗∗ 0.227∗∗∗ 0.215∗∗∗ (0.041) (0.039) (0.039) (0.034) (0.034) (0.035) Dummy Belgium/Luxembourg −0.010 −0.032 −0.030 0.007 0.019 0.023 (0.044) (0.040) (0.040) (0.036) (0.035) (0.035) Dummy Germany −0.041 −0.051 −0.045 0.008 −0.013 −0.005 (0.048) (0.045) (0.045) (0.039) (0.038) (0.038) Dummy Spain 0.100∗∗ 0.110∗∗ 0.104∗∗ 0.050 0.039 0.029 (0.047) (0.043) (0.044) (0.039) (0.037) (0.038)

Observations 594 598 594 598 594 594 598 594 594 R2 0.080 0.014 0.094 0.111 0.266 0.273 0.378 0.431 0.439 Adjusted R2 0.074 0.009 0.083 0.101 0.253 0.256 0.371 0.420 0.425 Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01